Prove that if $2n+1$ and $3n+1$ are both perfect squares then $40|n$.
72389
Positive integer $n$ such that $2n+1$ , $3n+1$ are both perfect squares
147848
Integer $x$ for which $x^4+x^3+x^2+x+1$ is perfect square.
55060
Prove that $n^2+n+41$ is prime for $n<40$
6488
Proof that $n^3 + 3n^2 + 2n$ is a multiple of $3$.
5257
Proving that $(3n)!$ is divisible by $n! \times (n + 1)! \times (n + 2)!$ if $n$ is greater than 2
143540
How to prove this decomposition of sum of squares?
103360
Prove $4p-3$ is a square knowing that $n\mid p-1$ and $p\mid n^3-1$, $p$ prime
118538
Find all integers $x$ such that $x^2+3x+24$ is a perfect square.
155784
If $\gcd(a, b) = 1$ and if $ab = x^2$, prove that $a, b$ must also be perfect squares; where $a,b,x$ are in the set of natural numbers
59479
For a positive integer $n\geq 2$ with divisors $1=d_1<d_2<\cdots<d_k=n$, prove that $d_1d_2+d_2d_3+\cdots+d_{k-1}d_k<n^2$
101832
Proof that sum of first $n$ cubes is always a perfect square
114810
$n!$ is never a perfect square if $n\geq2$. Is there a proof of this that doesn't use Chebyshev's theorem?
145519
Prove that for any natural number $n>1$, we have $(2n)!<(n(n+1))^n$
46102
Prove that $2^n +1$ in never a perfect cube
24820
Prove that if $n$ is a perfect square, then either $n \equiv 1 \pmod 4$, or $n \equiv 0 \pmod 4$.
35052
Prove that if $m^2 + n^2$ is divisible by $4$, then both $m$ and $n$ are even numbers.
57250
Proving that the sum and difference of two squares (not equal to zero) can't both be squares.