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Euler's formula for generating amicable pairs of integers is the following rule: = Suppose n> m > 1 are integers such that p 2m (2n-m+1) – 1, q = 2n (2n-m+1) – 1, and r = 2n+m (2n-m + 1) 1 are all prime numbers. Then a = = 2" pq and b = 2nr are amicable numbers. Prove that Euler's formula for generating amicable pairs of integers works. =

Euler's formula for generating amicable pairs of integers is the following rule: = Suppose n> m > 1 are integers such that p 2m (2n-m+1) – 1, q = 2n (2n-m+1) – 1, and r = 2n+m (2n-m + 1) 1 are all prime numbers. Then a = = 2" pq and b = 2nr are amicable numbers. Prove that Euler's formula for generating amicable pairs of integers works. =

Algebra & Trigonometry with Analytic Geometry
Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter1: Fundamental Concepts Of Algebra
Section1.1: Real Numbers
Problem 38E
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Euler's formula for generating amicable pairs of integers is the following rule: Suppose n > m > 1 are integers such that p = 2m (2n-m + 1) 1, q = 2n (2n−m + 1) − 1, and r = 2n+m (2n−m + 1) – 1 are all prime numbers. Then a = 2" pq and b 2nr are amicable numbers. Prove that Euler's formula for generating amicable pairs of integers works. =
Transcribed Image Text:Euler's formula for generating amicable pairs of integers is the following rule: Suppose n > m > 1 are integers such that p = 2m (2n-m + 1) 1, q = 2n (2n−m + 1) − 1, and r = 2n+m (2n−m + 1) – 1 are all prime numbers. Then a = 2" pq and b 2nr are amicable numbers. Prove that Euler's formula for generating amicable pairs of integers works. =
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