If $3n+1$ is a perfect square where $n$ is a positive integer greater than $1$. Then how to prove that $n+1$ would be sum of $3$ 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.
150088
Prove that $\sqrt {n − 1} +\sqrt {n + 1}$ is irrational for every integer $n ≥ 1$
56624
Prove that $0!+1! + 2! + 3! + ..... + n!$ $\neq$ $p^\text{r}$, where $n \geqslant 3$ and $n$, $p$ and $r$ are three integers
45911
Prove that none of $\{11, 111, 1111,\dots \}$ is the perfect square of an integer
145558
Prove that $2^n+3^n $ is never a perfect square
121036
Is there any perfect squares that are also binomial coefficients?
48787
A number is a perfect square if and only if it has odd number of positive divisors
50663
prove or disprove: For a prime number p, there is a positive integer n such that $p+1 $= $n^2$ if and only if $ p = 3.$
67968
When is $2^n -7$ a perfect square?
4750
Show that for any positive integer n, $(3n)!/(3!)^n$ is an integer.
67356
When is $2^x+3^y$ a perfect square?
72666
Prime Numbers And Perfect Squares
92106
Prove that $n$ is a sum of two squares?
95889
Prove that $\gcd(n! + 1, 3n! + 1) = 1$, $\forall n \in \mathbb{N}$, $n \geq 2$.
100375
Prove that ${\sqrt {n} }^{\sqrt {n+1}} > {\sqrt {n+1}}^{\sqrt {n}}$.
127566
$2AB$ is a perfect square and $A+B$ is not a perfect square
131625
Expressing an integer as the sum of three squares