give direct proof of the fact $a^2 - 5a + 6$ is even for any integer
130027
Give a direct proof of the fact that $a^2-5a+6$ is even for any $a \in \mathbb Z$
123267
Proving that even numbers equal the sum of two odd numbers.
25023
How do you prove that there are infinitely many primes of the form $5 + 6n$?
44528
The only natural number $x$ for which $x+\sqrt{-2}$ is a cube in $\mathbb{Z}[\sqrt{-2}]$ is $x=5$
42744
Prove a number is even using the Pigeonhole Principle
100558
Prove that for any even positive integer $n$, $n^2-1 \mid 2^{n!}-1$
129163
Showing that every positive integer can be represented in this form
40269
Proving if $x^3$ is even, then $x$ is even.
48484
Prove that $6|a+b+c$ if and only if $6|a^3+b^3+c^3$
105985
Prove that all even integers $n \neq 2^k$ are expressible as a sum of consecutive positive integers
127891
If $ a^{2} + b^{2} = c^{2}$ and $c$ is even, prove that $a$ and $b$ are both even.
100892
Proving divisibility of $a^3 - a$ by $6$
130342
Show that for any integer a and prime p, $(a+1)^p \equiv a^p+ 1 \pmod{p}$.
83935
Using congruences, show $\frac{1}{5}n^5 + \frac{1}{3}n^3 + \frac{7}{15}n$ is integer for every $n$
24160
Show that if $a$ is an odd integer and $b$ is an even integer then $\gcd(a,b)=\gcd(a,b/2)$
7491
How to show that $7\mid a^2+b^2$ implies $7\mid a$ and $7\mid b$?
133382
Proof that $a+b+\frac{1}{1+\sqrt{ab}}\geq\frac{5}{2}$