1. Let a and b be natural numbers, where a, b > 2, such that gcd(a, b) = 1 and ab = (x + y)" for some natural number n and integers x and y. Prove that x + y cannot be prime.
1. Let a and b be natural numbers, where a, b > 2, such that gcd(a, b) = 1 and ab = (x + y)" for some natural number n and integers x and y. Prove that x + y cannot be prime.
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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![1. Let a and b be natural numbers, where a, b > 2, such that gcd(a, b) = 1 and ab = (x + y)" for some natural number n and integers x and y. Prove that x + y cannot be prime.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F66318fc8-0ad6-4ce3-b166-594a4cfc43a5%2Fc2e3702c-bffd-4831-8d4e-b6542df9db62%2Fmkg5bo_processed.jpeg&w=3840&q=75)
Transcribed Image Text:1. Let a and b be natural numbers, where a, b > 2, such that gcd(a, b) = 1 and ab = (x + y)" for some natural number n and integers x and y. Prove that x + y cannot be prime.
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