$m^2+n^2$ and $m^2-n^2$ cannot both be squares
57250
Proving that the sum and difference of two squares (not equal to zero) can't both be squares.
103784
Show that $n^2+11n+2$ is not divisible by $113^2$ ( n is integer)
153100
A counterexample to "$k\mid n$ if and only if $k\mid n^2$"
115825
Unnesting $\sqrt{1+\sqrt2}$
80671
Product of sums of square is a sum of squares.
95588
Prove by Contradiction: if $4\mid a^2 + b^2$, then $a$ and $b$ are not both odd
57368
Prove that a positive polynomial function can be written as the squares of two polynomial functions
82630
How is it, that $\sqrt{x^2}$ is not $ x$, but $|x|$?
116307
Polynomial whose only values are squares
92599
Prove there generally is no isomorphism between $R[x]/(x^2-a)$ and $R^2$
136366
Show that if $2+2\sqrt{28n^2+1}$ is an integer then it must be perfect square.
53331
$\mathbb{Q}(\sqrt2, \sqrt3)$ is not isomorphic to $\mathbb{Q}(\sqrt[4]2)$
145558
Prove that $2^n+3^n $ is never a perfect square
67161
No maximum(minimum) of rationals whose square is lesser(greater) than $2$.
20964
Proof that $n^2 < 2^n$
112575
Finding integer solutions of $m^2-n^5 = m - n$
153444
$\mathbb{Q}(\sqrt[3]{2})$ is not in any cyclotomic extension of $\mathbb{Q}$