(adsbygoogle = window.adsbygoogle || []).push({}); 1. The problem statement, all variables and given/known data

Prove the following proposition: For any positive integers x and y, (x^2 - y^2) is not equal to 6.

2. Relevant equations

3. The attempt at a solution

I'll try to prove using contradition.

Assume x^2 - y^2 = 6.

(x+y)(x-y) = 6

(x+y)=6 and (x-y)=1 (OR)

(x+y)=1 and (x-y)=6 (OR)

(x+y)=-6 and (x-y)=-1 (OR)

(x+y)=-1 and (x-y)=-6 (OR)

(x+y)=2 and (x-y)=3 (OR)

(x+y)=3 and (x-y)=2 (OR)

(x+y)=-2 and (x-y)=-3 (OR)

(x+y)=-3 and (x-y)=-2

When I solve those equations, x and y turns out to be fractions.

Therefore, there is a contradition.

Therefore, (x+y)(x-y) is not equal to 6.

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Hi fellow physicsforumers

This is my first post. :D

I just started my discrete maths course at uni.

Is my solution correct?

Even if it is, is there any simpler way?

Thanks,

razefast

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# [Number Theory] Prove (x^2 - y^2) is not equal to 6.

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