Prove that $ 2^{6ℓ + 2} ≡ 4\pmod{18}$
102444
What is $26^{32}\bmod 12$?
12210
Show that $a^{61} \equiv a\pmod{1001}$ for every $a \in \mathbb{N}$
142338
Prove that $\lfloor\frac{n+1}{2}\rfloor+\lfloor\frac{n+2}{4}\rfloor+\lfloor\frac{n+4}{8}\rfloor+\lfloor\frac{n+8}{16}\rfloor+ \dots=n$
46814
$ a+b+c+d=6 , a^2+b^2+c^2+d^2=12$ $\implies$ $ 36 \leq 4(a^3+b^3+c^3+d^3)-(a^4+b^4+c^4+d^4) \leq48 $
152039
Prove that $a^{2^n}=1 \mod 2^{n+2}$
143754
Finding the solution of the congruence $4x\equiv16\pmod{26}$
146851
Prove that $-3$ is a quadratic residue mod an odd prime $>3$ if and only if $p$ is of the form of $6n+1$
48484
Prove that $6|a+b+c$ if and only if $6|a^3+b^3+c^3$
43478
Prove that: $ m_a + m_b + m_c \le 4R + r $
34323
Prove that $a^{(p-1)/2} \equiv 1$ (mod p) and $a^{(p-1)/2} \equiv -1 \pmod p$
121177
Prove that $\frac{(2a+b+c)^2}{2a^2+(b+c)^2}+\frac{(2b+c+a)^2}{2b^2+(c+a)^2}+\frac{(2c+a+b)^2}{2c^2+(a+b)^2} \le 8$
149508
Prove $9^n \equiv 9 \pmod{24}\quad \forall n \in \Bbb N^*$
79652
Proof by induction that $2 + 4 + 6 + \cdots + 2n = n(n+1)$
29989
Solve $x^2+5x+6 \equiv 0 \pmod{\!11\cdot 17}$
15210
Group of order 6 proof
15897
Solve a congruence $1978^{20}\equiv x\pmod{125}$
154722
How do I prove $2 \binom n2 + 4 \binom n4 + 6 \binom n6 + \cdots = n 2^{n-2}$