$3^m+7^n$ is a perfect square!!
138548
For what pair of integers $(a,b)$ is $3^a + 7^b$ a perfect square.
90962
For positive integers $m,n$ if $\sqrt 7 - \frac{m}{n} > 0$ then prove that $\sqrt 7 - \frac{m}{n} > \frac{1}{{mn}}$
125040
Show by induction : $n^7-n$ is a multiple of 7
35326
There are infinitely many $N$ such that $\frac{N}{2}$ is a perfect square, $\frac{N}{3}$ is a perfect cube, and $\frac{N}{5}$ is a perfect fifth power
84220
Questions on perfect squares
27387
Show that $a+b+c=0$ implies that $32(a^4+b^4+c^4)$ is a perfect square.
58264
How to derive the formula for the sum of the first $n$ perfect squares?
105564
If $n$ is a positive integer greater than 1 such that $3n+1$ is perfect square, then show that $n+1$ is the sum of three perfect squares.
39994
What is the largest perfect square that divides $2014^3-2013^3+2012^3-2011^3+\ldots+2^3-1^3$
145558
Prove that $2^n+3^n $ is never a perfect square
129238
Divisibility of $2^n - 1$ by $2^{m+n} - 3^m$.
87666
Find $n$ such that $n/2$ is a square, $n/3$ is a cube, and $n/5$ a fifth power
142580
Prove that a perfect square is either a multiple of $4$ or of the form $4q+1$.
102154
If $a$ and $b$ are consecutive integers, prove that $a^2 + b^2 + a^2b^2$ is a perfect square.
103504
Weird $3^n$ in an identity to be combinatorially proved
124685
How to show $(mn)!$ is divisible by $(m!)^n$?
87379
How to prove that $2^{n+2}+3^{2n+1}$ is divisible by 7 using induction?