Prove that for all integers $n$, $3$ does not divide $n^2-5$ using modular arithmetic.
139
Prove or disprove: For every integer a, if a is not congruent to 0 (mod 3), the a^2 is congruent to 1 (mod 3)
49299
Proof by Induction: For any integer $n > 0$, $3|(5^{2n} − 1)$.
129521
Is $\sqrt[3]{5}$ in $\mathbb Q(\sqrt[3]{2})$?
46741
Prove that $n$ divides $\phi(a^n -1)$ where $a, n$ are positive integer without using concepts of abstract algebra
9302
Questions about Divisibility of $2^n$ by $3$
23879
If $m$ and $n$ are distinct positive integers, then $m\mathbb{Z}$ is not ring-isomorphic to $n\mathbb{Z}$
52032
Prove that ${n^5 - n}$ is divisible by 5
133017
Prove that $n^n>1\times3\times5\times7\times \dots\times(2n-1)$
113119
Use the division algorithm to prove that 3|(n³ + 2n) for all n ∈ ℕ
98963
Prove that neither $A$ nor $B$ is divisible by $5$
21100
Simple Proof by induction: $9$ divides $n^3 + (n+1)^3 + (n+2)^3$
22973
Show that an integer of the form $8k + 7$ cannot be written as the sum of three squares.
117167
$3^{n+1}$ divides $2^{3^n}+1$
82913
Is this a proof of Fermat's Last Theorem where n = 3?
69039
Prove that $2730$ divides $n^{13} - n$ for all integers $n$.
139269
Prove that $2n-3\leq 2^{n-2}$ , for all $n \geq 5$ by mathematical induction
12694
Why does $a^n - b^n$ never divide $a^n + b^n$?