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Show that 1729 is a Carmichael number.

Discrete Mathematics and Its Applications | 7th Edition | ISBN: 9780073383095 | Authors: Kenneth Rosen ISBN: 9780073383095 37

Solution for problem 46E Chapter 4.4

Discrete Mathematics and Its Applications | 7th Edition

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Discrete Mathematics and Its Applications | 7th Edition | ISBN: 9780073383095 | Authors: Kenneth Rosen

Discrete Mathematics and Its Applications | 7th Edition

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Problem 46E

Problem 46E

Show that 1729 is a Carmichael number.

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Notes: The presidency Continued 3/3/16 What the president does Powers of the presidency: Express Powers Implied Powers Inherent Powers Delegated Powers Express powers: - Powers relative to constitution - Listed in the constitution on what the president can do - State of UnionAddress (Opportunity to say how things are going) - Commander in chief ofArmed Forces (War PowersAct 1973) - Make treaties (negotiation) - Receive ambassadors - Appoint judges and Other Officers - Recommend (not pass) laws - Veto power The WHOLE legislation or not Line Item Veto = If he received a big piece of legislation he can cross off parts (PRESIDENT DOESNT HAVE THIS POWER) Implied Powers: - “Executive Power” > Execute laws - “Take care Clause” - Mere Designation (Madison Taft): Written how president is supposed to do it exactly - General Grant (Hamiltonian Model): Powerful executive World/Economic Conditions: - Industrial Revolution (transportation, communication, world became faster) - WW1 - Great Depression Limits on the “General Grant” - Two Limits: 1. If congress says NO the president CAN’T act 2. President must execute all laws, not just the ones he likes Important Implied Powers: Executive orders executive agreements executive privilege executive immunity Executive Orders: - Rule or order issued by the president to an executive branch of the government and enforcing law ExecutiveAgreement: - International agreement, usually regarding routine administrative matters not warranting a formal treaty, made by the executive branch of the US government without ratification by the Senate Executive privilege: - Important = secret - - Rules that doctors cannot talk about your case with other people Priests don’t have to testify any bad things confessed to them Notes: The presidency Continued 3/3/16 What the president does Executive Immunity: - Immunity granted to officers of executive branch of government from personal liability for tortious acts or omissions done in the course of carrying out their duties. Implied Powers: - Implied by the constitution - Nothing to do with the constitution - Derives from the fact that you are the executive, head of state - Foreign affairs to use this power (Regulate out relations with all other countries) Delegated powers: - New Deal: Congress gave vast amounts of power to president - Rise ofAdministrative State: Growth has become unmanageable for congress to make detailed legislation - “Intelligible principle” >>>> Guidance on what the president is supposed to accomplish How - Executive Order: Legislating around congress - Agency Rule-Making: Most important, KEYTHINGS THAT BUREAUCRACY DOES Monday, February 29, 2016 Presidency Continued Political Science: Assessing Presidential Performance: - Presidential Charisma is important, performance is a large part contingent on the president’s power to PERSUADE - All presidents face a similar institutional context: They share power over policy development with Congress and the Supreme Court, they oversee a large federal bureaucracy with administrative discretion over policy implementation, they often face a decision of divided government…These actors and institutions structure the ability of presidents to pursue their policy goals. The power to persuade is the power to bargain! - They utilize the books of the office to persuade the public and other branches of government to follow their lead - The president’s performance is directly related to the power to persuade - Abraham Lincoln ranked first in leadership characteristics - The ACTIVE POSITIVE personality type is the best for the president The presidency Learning Objectives Chapter 9: 1. Presidents have three primary goals while in office: to achieve good public policy, to win reelection, and to be historically relevant. Congress plays an important role in each. 2. Because the Constitution is is vague on presidential power, it varies, greatly from president to president. (social responsibility) 3. Leadership of the public is the preeminent governing strategy of contemporary presidents (communication) 4. Presidential decision making is a complex process with many variables to be considered (personal responsibility) President’s 3 primary goals: - All three goals tie directly to the president’s relationship with congress - Set goals > Accomplish goals - Dealing with congress, ability to bargain with legislators, pick right issues to prioritize and act quickly before his honeymoon period wanes. - When there are more members of the president’s party in Congress, the president is more likely to be successful in dealing with Congress - TIMING is important Tuesday, March 1, 2016 Because the constitution is Vague on presidential power, it varies greatly from president to president - As commander in chief the president decides in US foreign policy - Persuasion most often happens when presidents bargain with legislators to achieve their legislative goals - Presidential power is about strategy, taking advantage of circumstances favorable to the president - If the president has HIGH public ratings, he should tackle a difficult problem White House Organization: - The power of the presidency has expanded beyond a literal interpretation of the US constitution, it also extends beyond what the president can do individually. - The president today has assistance from immediate advisors and bodies of policy experts - They can accomplish more with the help from the size and scope of the White House Organization - Con: Multiple advisers, especially at high levels, make it difficult to hold anyone accountable when the White House makes mistakes - White House staff members represent the president’s views accurately and thus serve as a direct extension of the president’s own views - Best way to influence public opinion >>>> TELEVISED ADDRESS - Presidents more often see their approval ratings decrease following their state of Union address - If misery index is relatively high, presidential approval ratings tend to be low - Approval ratings tend to be high at the beginning of a presidential administration AND tend to decline during presidential term Choosing the president: - Primaries and Caucuses: Designed to decide who the democrats and republicans will be, leads to conventions > super Tuesday - Primary (Election): tally votes - What happens at Caucuses: big room, representative from each candidate in the room, people separate into corners to be counted (Represents democratic democracy) - Problems with Caucuses: Long, chaotic, difficult for people with jobs, elderly, people with children - General election - Electoral college 3/1/16 Delegates at Stake today: - Republicans 595 (up for grabs) 1237 needed to win - Democrats 865 (up for grabs) 2383 needed to win Often have more super delegates > Not chosen through the primary or caucus process Electoral College - President can win even if the public votes against them if the electoral college gets the majority Win ELECTORAL COLLEGE lose POPULAR VOTE Vice president: - Electoral value - Special projects - Votes on a tie First Lady - Diplomatic importance - electoral value: Out campaigning for you - special projects Book notes: The presidency 2/26 Central Ideas: - President has many roles of responsibilities - Power of presidency has grown - Executive power is limited - Presidential personality and character matter President vs. Presidency: - Common to judge the performance of an individual president through his term in office - Constitution does not specify who the president should be - Constitution DOES establish eligibility qualifications, term length, limitations, and the circumstances and procedures for replacing the president - President must be at least 35 years born citizen who has resided in the US for 14 years. - Term length of president and vice president, 4 years! - Impeachment: official from public office by force, occurs when a legislative body votes to bring charges against the individual, treason, bribery, high crimes and misdemeanors - 25th amendment establishes that vice president shall become president President’s roles and responsibilities: - Expressed powers: Granted to him by the Constitution - Implied powers: Powers not expressly stated in the constitution but have been interpreted by the presidents as necessary to faithfully execute the laws and protect and defend the constitution - Delegated powers: delegated to president by congress in order to implement legislation Implied presidential power: Issuing executive orders Expressed presidential power: Granting pardons and Reprieves Executive Power in the President: - He is in charge with making sure laws passed by congress are “faithfully executed” which he does with the help of the federal bureaucracy - Federal Bureaucracy: The departments, bureaus, agencies and offices of the executive branch of government that are characterized by hierarchal organization and the assignment of specific job responsibilities of employees - He is allowed to establish federal departments in the executive branch and to appoint their organization heads, known as secretaries to implement the law - Reorganizing the government to best meet their management styles and achieve their policy goals CEO: - Think of the president as the CEO of a company, his job is to ensure that all of his staff are meeting the goals of the company Management styles of presidents (executive): - One of the most POWERFULtools of administration: The president’s right to appoint the heads of federal departments (with the advice and consent of the senate) - Why are the appointments important > He is able to reprioritize the policy goals of each - department Executive Power Clause: Grants the president the authority to carry out all laws passed by congress the vague language by this clause has been used by presidents to significantly expand the powers of office - Executive orders are declarations issued by the president that relate to the organization of the federal bureaucracy, the execution of federal legislation and the enforcement of federal court decisions. > Derived from the presidential oath of office and the executive power clause - Executive Privilege:Act of withholding information from congressional, judicial or public scrutiny Book notes: The presidency 2/26 Legislative powers of the president: - The president’s legislative responsibilities include the power to Veto legislation and the ability to shape the legislative agenda through the state of Union address. - AFTER house and senate vote on a bill they submit it to president for his review - State of union address: President reports to congress from time to time to see what he would sign - President’s veto power is derived fromArticle 1 of the constitution - Republican congress and democratic president = large number of vetoes - Vice president: vote in senate if there is a tie Judicial Power of the President: - His ability to nominate justices to the courts and to grant pardons, deprives, and amnesties fives him a check over judicial power - Article II section 2 establishes the president’s power to nominate justices to the Supreme court and other federal courts by congress - Senate Conformation: approval by 2/3 of the senators present, of a presidential nominee - The president EXERCISES judicial power through the granting of pardons, reprieves, and amnesty for crimes committed against the United States - Watergate scandal: Major Political Scandal following a break-in at the Democratic National Committee headquarters at the watergate office complex in Washington DC, Nixon’s administrations attempted to cover up his involvement - The scandal led to the discovery of multiple abuses of power by the Nixon Administration - At the end of his term as president what power would the president most likely utilize: Granting a pardon to a convicted criminal - Presidential check on judicial power: Granting amnesty to a group of people. - Pardon: The exoneration of both the crime and the associated penalty - Reprieves: The exoneration of the penalty associated with a crime, BUT not the crime itself - Amnesty:Apardon that is issued to a group of people who are not in compliance with the law Diplomatic Powers: - Ratification: formal and legal binding approval - Substitution for a treaty ratified by the senate is an EXECUTIVEAGREEMENT - The president might use the power to receive foreign dignitaries and appoint US ambassadors in order to recognize the legitimacy of other nations Power of president has grown: - Globalization: The spread and integration of economics, politics, technology, and culture around the world Military Powers: - The president is the highest ranking officer in the US armed forces - - Commander in chief of the Military - Power to declare War The last time congress declared war was WW2 (1941) Policies and Programs: - Commerce Clause: Enumerated power from article 1 and 8 of the constitution that grants congress the authority to regulate commerce. This has provided the basis for expanded national power through federal legislation on a broad array of issues - The Executive branch has expanded in part due to the growth in policies and programs that must be administered by the federal bureaucracy. - The primary focus of government policies and programs between the 1780s and the 1930s: Commerce between states and with other nations Book notes: The presidency 2/26 - The executive branch created a number of new bureaucracies after the Great Depression Political Parties and Mass Media - The development of political parties and mass media have strengthened the connection between the American Public and the president - The expansion of mass media in all forms has further strengthened the connection between the president and theAmerican people by allowing him to appeal directly to the public through press conferences and public events. - Strategy of “GOING PUBLIC” >>> Magazines, newspapers, radio, television, and the Internet have come to reach nearly every american home so the president can appeal directly to the public this way - What would represent an instance of the president “going public” CIRCUMVENTING congress to petition the people directly Globalization: - The US role as a world leader has the consequence of ripple effects from the domestic economic - activity Globalization and technological process have had increase in presidential power Presidential Interpretation and Congressional Delegation - Presidency power has expanded based on interpretation of responsibilities suggested by the presidential oath of office - Congress shifted power to the executive branch over time - Limited power of the executive branch in fear of tyranny Executive Power is Limited: - President depends on congress for conformation of department heads, approval of administrative budgets, and appropriation of government resources to keep his departments and offices in business - Implied powers: General powers suggested by the constitution rather than specifically enumerated with it - DECLARING WAR IS LIMITED FOR THE PRESIDENT - The senate holding a cote on a Supreme Court nomination would be considered a check on presidential power

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Chapter 4.4, Problem 46E is Solved
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Textbook: Discrete Mathematics and Its Applications
Edition: 7
Author: Kenneth Rosen
ISBN: 9780073383095

The answer to “Show that 1729 is a Carmichael number.” is broken down into a number of easy to follow steps, and 7 words. Discrete Mathematics and Its Applications was written by and is associated to the ISBN: 9780073383095. The full step-by-step solution to problem: 46E from chapter: 4.4 was answered by , our top Math solution expert on 06/21/17, 07:45AM. This full solution covers the following key subjects: carmichael, show. This expansive textbook survival guide covers 101 chapters, and 4221 solutions. Since the solution to 46E from 4.4 chapter was answered, more than 359 students have viewed the full step-by-step answer. This textbook survival guide was created for the textbook: Discrete Mathematics and Its Applications, edition: 7.

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Show that 1729 is a Carmichael number.