Sum of odd numbers always gives a perfect square.
42831
How to derive the formula for the sum of the first $n$ odd numbers: $n^2=\sum_{k=1}^n(2k-1).$
5692
Proving that there is a perfect square between $n$ and $2n$
142513
Prove that $2xy\mid x^2+y^2-x$ implies $x$ is a perfect square.
44790
Find $n$ for which $\frac{n(n+1)}{2}$ is perfect square
67356
When is $2^x+3^y$ a perfect square?
143271
Finite sum of reciprocal odd integers
106716
The sum of square roots of non-perfect squares is never integer
149481
Number theory counting sums of squares modulus
8034
Can $n!$ be a perfect square when $n$ is an integer greater than $1$?
94019
Find all $p$'s such that $p^4 + p^3 + p^2 + p +1$ is a perfect square.
151508
How to determine number with same amount of odd and even divisors
138259
Proof or disproof that every integer can be written as the sum of a prime and a square.
45911
Prove that none of $\{11, 111, 1111,\dots \}$ is the perfect square of an integer
78593
Prove that the product of four consecutive positive integers plus one is a perfect square
7414
Prove that odd perfect square is congruent to $1$ modulo $8$
48787
A number is a perfect square if and only if it has odd number of positive divisors
19588
$n!+1$ being a perfect square