Show that $2^n \not \equiv 1 \pmod n$
33866
Show that $n$ does not divide $2^n - 1$ where $n$ is an integer greater than $1$?
32762
Proof for: $(a+b)^{p} \equiv a^p + b^p \pmod p$
5043
Show that $2^n>1+n\sqrt{2^{n-1}}$
75166
Find with proof all positive integers $n$ such that $2^n + 1 \equiv 0 \pmod{n}$
91935
If $x \equiv a \pmod {p_1}$ and $x\equiv a \pmod{p_2}$, then is it true that $x\equiv a \pmod{p_1p_2} ?$
24820
Prove that if $n$ is a perfect square, then either $n \equiv 1 \pmod 4$, or $n \equiv 0 \pmod 4$.
44033
Number theory lemma - $x^2 \equiv 1 \pmod p$ implies $x\equiv\pm 1\pmod p$
10105
Proving $\, a^b = (a\bmod n)^b\, \pmod{\!n}\ $ [Congruence Power Rule]
47060
Split $n$ into nontrivial factors via a nontrivial square-root of $1\!\pmod{\!n}$
8609
Prove by induction that $n!>2^n$
55266
Prove that $(n+1)^{n-1}<n^n$
143772
How can I algebraically prove that $2^n - 1$ is not always prime?
96152
Showing that $a^n - 1 \mid a^m - 1 \iff n \mid m$
29640
If $x \equiv 1 \pmod 3$ and $x \equiv 0 \pmod 2$, what is $x \pmod 6$?
121706
Show $\text{det}(A)$ is divisible by $2^{n-1}$
51858
Showing $\gcd(2^m-1,2^n+1)=1$
124685
How to show $(mn)!$ is divisible by $(m!)^n$?