8. Let p be an integer such that p≥ 2. Suppose that for all x, y = Z, if p|xy then pr or ply. Prove that p is prime. (This is the converse of the "Theorem on Division by a Prime.")
8. Let p be an integer such that p≥ 2. Suppose that for all x, y = Z, if p|xy then pr or ply. Prove that p is prime. (This is the converse of the "Theorem on Division by a 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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Transcribed Image Text:8. Let p be an integer such that p≥ 2. Suppose that for all x, y € Z, if p|xy then px
or ply. Prove that p is prime. (This is the converse of the "Theorem on Division by a
Prime.")
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