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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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 ?
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