Answered: If x, y, z e N, and x² – y² = x + y,…

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If x, y, z e N, and x² – y² = x + y, prove x = y + 1.

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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Question

Please don't do it for z=2,

It's a trivial solution for z = 2 and getting the desire relation x = y + 1. But if z = 1 or (other natural numbers of z than can be prove later on) you will get y = 0, x = 1. But the problem is, 0 is not a natural number ℕ as stated in the problem.

I am totally stuck

If x, y, z e N, and
x² – y² = x + y,
prove x = y + 1.

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