If $3n+1$ and $4n+1$ are perfect squares prove that $n$ is divisible by $56$.
60738
If 4n+1 and 3n+1 are both perfect sqares, then 56|n. How can I prove this?
38904
Prove that $(a + b + c)^{13}$ is divisible by $abc$ if $b|a^3$, $c|b^3$ and $a|c^3$.
19588
$n!+1$ being a perfect square
21906
Show $3^m + 3^n +1$ cannot be a perfect square for $m,n$ being positive integers.
94019
Find all $p$'s such that $p^4 + p^3 + p^2 + p +1$ is a perfect square.
44790
Find $n$ for which $\frac{n(n+1)}{2}$ is perfect square
26336
Prove that $n(n^2 - 1)(n + 2)$ is divisible by $4$ for any integer $n$
3611
How to prove $n^5 - n$ is divisible by $30$ without reduction
68561
How to show $\lceil ( \sqrt3 +1)^{2n}\rceil$ where $n \in \mathbb{ N}$ is divisible by $2^{n+1}$
124816
Using the fact that $n^3 + 5n$ is divisible by $6$, infer that $n^4 - 2n^3 + 11n^2 + 14n$ is always divisible by $24$
128306
Show that for all $n ∈ Z$, $2n^3 + 3n^2 + n$ is divisible by both 2 and 3.
24446
Prove that for each $n$, there exist $n$ consecutive integers, each of which is divisible by a perfect square larger than $1$.
77816
Proof problem: Show that $n^2-1$ is divisible by $8$, if $n$ is an odd positive integer.
86285
Given positive integers $ x , y$ and that $3x^2 + x = 4y^2 +y$ Prove that $x-y$ is a perfect square
35666
How to prove the divisibility rule for $3\, $ [casting out threes]
134149
$z^n=(z+1)^n=1$, show that $n$ is divisible by $6$.
136964
Prove there exist 135 consecutive integers that each have a perfect cube $>1$ that divides it.