Prove (15n+17,10n+11) = 1
95036
For any integer $a$, $\gcd(11a+5,2a+1)=1$.
55266
Prove that $(n+1)^{n-1}<n^n$
111098
Prove $2^{2n} = \sum_{k=0}^{n}\binom{2n+1}{k}$
31708
Divisibility criteria for $7,11,13,17,19$
113290
Prove combinatorics identity
18914
How prove this $A=\left(B-\frac{1}{110}I\right)^T\left(B+\frac{1}{110}I\right)$
42360
Find the number of solutions of $a_0+a_1+a_2=17$ if $2\le a_0\le 5$, $3\le a_1\le 6$, $4\le a_2\le 7$.
99052
Prove that $( 1 + n^{-2}) ^n \to 1$.
145889
Prove if $56x = 65y$ then $x + y$ is divisible by $11$
6488
Proof that $n^3 + 3n^2 + 2n$ is a multiple of $3$.
5358
How to prove that 2017 divides $1^{2017}+2^{2017}+\dots+2017^{2017}$?
85287
Prove that, for $p > 3$, $(\frac 3p) = 1$ when $p \equiv 1,11 \pmod{12}$ and $(\frac 3p) = -1$ when $p \equiv 5,7 \pmod{12}$
102334
How can you prove $\frac{n(n+1)(2n+1)}{6}+(n+1)^2= \frac{(n+1)(n+2)(2n+3)}{6}$ without much effort?
83935
Using congruences, show $\frac{1}{5}n^5 + \frac{1}{3}n^3 + \frac{7}{15}n$ is integer for every $n$
113119
Use the division algorithm to prove that 3|(n³ + 2n) for all n ∈ ℕ
89175
Proof of $(a+b)^{n+1}$
66016
Prove $3^{2n+1} + 2^{n+2}$ is divisible by $7$ for all $n\ge0$