How to know if a sum of squares has integer solutions?
98408
Show that $x^2+y^2+z^2=999$ has no integer solutions
112575
Finding integer solutions of $m^2-n^5 = m - n$
80671
Product of sums of square is a sum of squares.
18245
How to check if a system of congruence is solvable?
152754
When is the sum of divisors a perfect square?
107448
proving that there is no solution for $n$ in positive integers except $n = 1$ for $2^n = nk + 1$
135458
When is a sum of consecutive squares equal to a square?
40525
Fastest way to determine if an integer's square root is an integer
2932
How do I prove this sum is not an integer
104917
Is $\sqrt1+\sqrt2+\dots+\sqrt n$ ever an integer?
93572
How to determine if $n (n \geq 2)$ given numbers can be summed up to a certain number?
73079
Eliminating non-integer solutions to $ab / (2\sqrt{ab} + a + b)$
147562
Sum of squares diophantine equation
8034
Can $n!$ be a perfect square when $n$ is an integer greater than $1$?
142978
combinatorics: sum of product of integer compositions
146333
Gaussian proof for the sum of squares?
19588
$n!+1$ being a perfect square