## 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

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