How to prove that the difference of squares of two natural numbers can't be a perfect square if their sum is a perfect square?
12732
Do any (non-trivial) 2-chains of Pythagorean triplets exist?
71935
Let $k$ be a natural number . Then $3k+1$ , $4k+1$ and $6k+1$ cannot all be square numbers.
27387
Show that $a+b+c=0$ implies that $32(a^4+b^4+c^4)$ is a perfect square.
22840
The sum of the first $n$ squares is a square: a system of two Pell-type-equations
23830
Proof that if $p\equiv3\,\left(\mbox{mod 4}\right)$ then $p$ can't be written as a sum of two squares
58264
How to derive the formula for the sum of the first $n$ perfect squares?
24601
Proving that a natural number made entirely of 6's and 0's is not a square.
131731
Primes that can't be written as sum of two squares. Mod
114810
$n!$ is never a perfect square if $n\geq2$. Is there a proof of this that doesn't use Chebyshev's theorem?
143540
How to prove this decomposition of sum of squares?
146241
If $a \in \Bbb Z$ is the sum of two squares then $a$ can't be written in which of the following forms?
8034
Can $n!$ be a perfect square when $n$ is an integer greater than $1$?
39156
Concerning what is between two consecutive squares.
142580
Prove that a perfect square is either a multiple of $4$ or of the form $4q+1$.
19588
$n!+1$ being a perfect square
65965
Theoretical way to prove no positive integer $n$ exists such that $n+3$ and $n^2+3n+3$ are both perfect cubes.
50596
$p_1p_2...p_n +1$ is not square for $p_k = k$'th prime