My problem is:

Prove that there are no integers x and y such that x^2 − 5y^2 = 2.

Hint: consider this equation modulo 5.

I don't get how to start this with using modulo 5.

do I make the whole equation divisible by 5?

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- Oct 11th 2010, 02:16 PMguyonfire89Modular Help
My problem is:

Prove that there are no integers x and y such that x^2 − 5y^2 = 2.

Hint: consider this equation modulo 5.

I don't get how to start this with using modulo 5.

do I make the whole equation divisible by 5? - Oct 11th 2010, 03:40 PMTraveller
Consider all possibilities. x will be one of the following :

a) 5k

b) 5k-1

c) 5k-2

d) 5k+1

e) 5k+2

for some suitable k.

What remainders do these leave when squared and divided by 5 ?