If $a$ is an odd positive integer $>$ $2$ such that 3 $\not$ | $a$, then $12$ $|$ $(a^2 -$1 ))
114873
Show that if $n$ is not divisible by $2$ or by $3$, then $n^2-1$ is divisible by $24$.
21531
The number of nonnegative integer triples with sum equal to $12$
138193
Why is $\sqrt {12} = 2 \sqrt 3$?
17047
Prove that if n is even then $n^2$ is even and if n is odd then $n^2$ is odd?
113168
If $a > b$, is $a^2 > b^2$?
91105
For every $n\ge3$ there exists $n$ different integers $a_1,...,a_n$ so that $\frac{1}{a_1}+\frac{1}{a_2}+...+\frac{1}{a_n}=1$
24160
Show that if $a$ is an odd integer and $b$ is an even integer then $\gcd(a,b)=\gcd(a,b/2)$
96097
Let $k$ be an odd positive integer. Prove that $(1+2+3...+n)|(1^k+2^k+3^k+...+n^k)$ for all positive integers $n$.
118629
$p,q$ odd primes, $q\mid a^p-1\Rightarrow q\mid a-1$ or $\,2p\mid q-1$
77806
Proving if $a$ is not a multiple of prime $p$, then an integer $b$ exists such that $p^b - 1$ is a multiple of $a$
74561
Let $a_1,a_2,\cdots,a_n$ be $n$ numbers such that $a_i$ is either $1$ or $-1$.If $a_1a_2a_3a_4+\cdots+a_na_1a_2a_3=0$ then prove that $4\mid n$.
95588
Prove by Contradiction: if $4\mid a^2 + b^2$, then $a$ and $b$ are not both odd
513
If n is an odd integer, show there exists a positive integer k such that 2^k mod n = 1.
47232
Prove $\forall a,b,c \in \mathbb Z$, if $ab+ac\equiv 3\pmod 6$ then $b \not\equiv c \pmod 6$ by contraposition
64052
Among any three consecutive positive integers one is a multiple of 3
85272
$3x + 1$ is even iff $5x-2$ is odd
146851
Prove that $-3$ is a quadratic residue mod an odd prime $>3$ if and only if $p$ is of the form of $6n+1$