Proof that $41$ does not divide $a^5 - 2$
93820
Fermat's little theorem applied for $n$'th root existence $\!\bmod p$
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)
96268
Prove that $5$ divides $3^{3n+1}+2^{n+1}$
8364
To show that Fermat number $F_{5}$ is divisible by $641$.
46741
Prove that $n$ divides $\phi(a^n -1)$ where $a, n$ are positive integer without using concepts of abstract algebra
142263
Assuming $ab^2 = b^3a$ and $a^2=1$ prove that the order of $b$ is $5$.
60615
Product of $5$ consecutive integers cannot be perfect square
28957
Verifying that $2^{44}-1$ is divisible by $89$
69902
$3$ never divides $n^2+1$
50894
Prove that $6$ divides $n(n + 1)(n + 2)$
148455
Show that if $(a,n)=d>1$ and $k$ is any positive integer, then $a^k\not\equiv 1\pmod{n}.$
100892
Proving divisibility of $a^3 - a$ by $6$
154133
Flawed proof by induction that $a^{n-1}=1$
29874
Not divisible by $2,3$ or $5$ but divisible by $7$
16642
Showing $a_n=\sin(n)$ does not converge
99631
Prove/Disprove: Find $a\in S_4$ that is not a power of $b$ such that $ab=ba$ while $b=(123)$
40626
Suppose that $ a,b \in \mathbb{Z}$ If 4 divides $ a^2 + b^2$, then $a$ and $b$ are not odd.