Proof that $a(1) \equiv 0 \pmod{q} \Rightarrow (x-1)|a(x)$
10254
Is the Polynomial Factor Theorem true over all commutative rings?
91935
If $x \equiv a \pmod {p_1}$ and $x\equiv a \pmod{p_2}$, then is it true that $x\equiv a \pmod{p_1p_2} ?$
62382
I suppose $(a,m)=(a-1,m)=1$, show that $1+a+a^2+\ldots+a^{\phi(m)-1}\equiv0\pmod m$
80009
Prove that $| |a|-|b| | \le |a-b|$
29204
$a\equiv\bar a\!\pmod{\!kn}\Rightarrow a\equiv\bar a\!\pmod{\! n};\ $ $(a\bmod kn)\bmod n=a\bmod n.\ $ Congruences persist mod factors of the modulus
112390
Solutions of $x^2 \equiv 1 \pmod N$
134384
What does $\rightarrow$ mean in $p \rightarrow q$
35236
Proof $p \vdash q \Rightarrow p$
104484
Prove that $r$ is a primitive root modulo $p$ if and only if $r^{(p−1)/q}\not\equiv 1\pmod{p}$
137511
Trying to show that $\sup \{b^p:p\in Q,\;0<p<x\} = \inf\{b^q:q\in Q,\;x<q\}$
36043
If $ab \equiv r \pmod{p}$, and $x^2 \equiv a \pmod{p}$ then $y^2 \equiv b \pmod{p}$ for which condition of $r$?
138107
Showing that $\left|\frac{z-a}{1-\bar{a}z}\right|=1$
41895
Show $\text{Hom}_{Ab}(A,\mathbb{Q}) = \{0\}$ for finite $A$
35897
Proof of: $AB=0 \Rightarrow Rank(A)+Rank(B) \leq n$
26478
Show that the congruence $x^{p-1} \equiv 1 \pmod {p^2}$ has precisely $p-1$ solutions modulo $p^2$
59442
Are there $a,b>1$ with $a^4\equiv 1 \pmod{b^2}$ and $b^4\equiv1 \pmod{a^2}$?
5708
Prove that if $k\ge 1\,$ and $\,a^k\equiv 1\pmod{\! n}$ then $\gcd(a,n)=1$