Either $np$ is even, or $n^2 − p^2$ is a multiple of $8$.
63774
If a and b are odd integers, then $8\mid (a^2-b^2)$
48787
A number is a perfect square if and only if it has odd number of positive divisors
153532
Proving $a^2$ is even $\implies$ $a$ is even by contradiction
1522
Is $\sqrt{64}$ considered $8$? or is it $8,-8$?
2731
Groups of even order have an element whose order is 2.
58935
If $p$ and $p^2+8$ are both prime numbers, then $p^3+4$ is prime.
377
Problem involving many squares and several variables.
76405
Let n be an even integer. How many different ways can I choose subsets of the set {1,2...,n}
156242
As many even numbers as natural numbers.
95588
Prove by Contradiction: if $4\mid a^2 + b^2$, then $a$ and $b$ are not both odd
43764
Prove $P_m X P_n$ is Hamiltonian if and only if at least one of $m,n$ is even
5692
Proving that there is a perfect square between $n$ and $2n$
119146
How to solve $n < 2^{n/8}$ for $n$?
92106
Prove that $n$ is a sum of two squares?
44182
Proving that an integer is even if and only if it is not odd
125040
Show by induction : $n^7-n$ is a multiple of 7
127901
If $x^2+y^2 \equiv 0\pmod{p}$, then $p \equiv 1 \pmod{4}$