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How to Prove a Theorem

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A simple theorem from number theory is proven to illustrate the concept of proof. Specifically, we prove that

For every n>2, there exist integers x, y such that x is congruent to y mod(n) and x is not congruent to -y mod(n).

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Solution Summary

In this solution,a simple theorem from number theory is proven to illustrate the concept of proof.

Solution Preview

For this problem, it is enough to find two integers x, y that satisfy the assertion of the theorem. It suffices to take:

(1) x = 1, and y = 1.

Clearly, 1 ...

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