# Indirect Proof of Rationals

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#1
I was solving a problem. Stumbled upon a totally irrelevant problem. Found an awesome proof for it. The proof is very similar to another famous proof (won't say which one). Try it!

Prove that there don't exist any non-integer rational numbers such that are all integers.

EDIT: apparently an easier proof exists too
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3 years ago
#2
Assume that are non-integer rationals with all integer. Then and are integers and have to be odd. So is odd. But we know that is an integer so is divisible by four. Contradiction.
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#3
(Original post by Zacken)
Assume that are non-integer rationals with all integer. Then and are integers and have to be odd. So is odd. But we know that is an integer so is divisible by four. Contradiction.
Yea. I found a much more indirect proof which was similar to proving is irrational. Basically assume are rationals in simplest form and then arrive at contradiction.
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