If x is an odd number, how to prove $x^2=8y+1$?
72511
If $n$ is an odd natural number, then $8$ divides $n^{2}-1$
104688
How can I prove that $x-{x^2\over2}<\ln(1+x)$
44182
Proving that an integer is even if and only if it is not odd
97411
If $x^n=y^n$ and $n$ is odd then $x=y$
151508
How to determine number with same amount of odd and even divisors
6165
Proof by Induction $n^2+n$ is even
59653
$x^2-y^2=2s$, s cannot be an odd integer
86285
Given positive integers $ x , y$ and that $3x^2 + x = 4y^2 +y$ Prove that $x-y$ is a perfect square
7466
How would I prove that if an integer $n>2$, then $\bar{z}=z^{n-1}$ has $n+1$ solutions
156641
Show that $\gcd(3n,3n+ 2) = 1$ when $n$ is odd
95588
Prove by Contradiction: if $4\mid a^2 + b^2$, then $a$ and $b$ are not both odd
6160
How to prove a number $a$ is quadratic residue modulo $n$?
128377
Mathematical Induction and "the product of odd numbers is odd"
125274
For $x+y=1$, show that $x^4+y^4\ge \frac{1}{8}$
81671
Proof of identity $\sqrt {xy} = \sqrt x \sqrt y$ for $x,y \in \mathbb R^+$
11506
Alternative proof that $(a^2+b^2)/(ab+1)$ is a square when it's an integer
20486
Numbers representable as $x^2 + 2y^2$