httpsgyazocom0e5d839a47a60eaade8c352b3b6086cf PROVE BY CONTR

https://gyazo.com/0e5d839a47a60eaade8c352b3b6086cf

PROVE BY CONTRADICTION.

Solution

Answer:

comsider the numbers 2 · 10^500 +15 and 2 · 10^500 +16

let us assume that these two numbers are perfect squares.

But we have only two perfect squares 0 and 1 whose difference is 1 .

Therefore these two consecutive integers cannot both be perfect squares.

This is a non-constructive proof.

we do not know which of them meets the requirement.