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Solutions for Elementary Number Theory | 7th Edition | ISBN: 9780073383149 | Authors: Professor David Burton 9780073383149

Solution for problem 2 Chapter 14

For n = 1, 2, ... , 10, show that 5u + 4(-l)n is always a perfect square

Elementary Number Theory | 7th Edition


Problem 2

For n = 1, 2, ... , 10, show that 5u + 4(-l)n is always a perfect square

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Week 1 BASICS REWIEW Arithmetic:  a+b=b+a  a+b +c=a+(b+c)  ab+c =ab+ac  ab=ba  ab)c=a(bc) Multiplying Fractions: a c ac  × = b d bd Dividing Fractions:  a÷ = ad b d bc Adding Fractions: a+ = ad+cb= ad+bc  b d bd bd bd Exponent Basics:  an means multiply a by itself n times  0 =0wheren>0 0  a =1wherea≠0  0 isindeterminate a = 1 wherea≠0  an becau0e n−n n −n 1=a =a =a a 1=a a−n 1 =a−n an Laws of Exponents: Given m & n are integers and a & b are real numbers:  a a =a m+n m a m−n  n =a wherea≠0 a

Chapter 14, Problem 2 is Solved

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For n = 1, 2, ... , 10, show that 5u + 4(-l)n is always a perfect square