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Prove $x^2 + 2y^2 \neq 805, x,y\in\mathbb{Z}$, using equivalence classes modulo 5
Prove $x^2 + 2y^2 \neq 805, x,y\in\mathbb{Z}$.
We did this in class and, for the life of me, I cannot remember how to finish the problem.
It starts out by taking all of the values to be $\mod5$.
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how to show equivalence relation and its classes
i am stumbling again in proving things in maths. the task is to prove that this statement
$A \sim B : \Longleftrightarrow \sum_{a\in A} a = \sum_{b\in B} b $
is an Equivalence Relation on Power Set ...
