Nov 10, 2025 · For example, $10^ {21}+1$ has some $192$ divisors, but all are congruent to $1$, $7$, $9$, $11$, $13$, $19$, $23$, or $37$ $\pmod {40}$. I have done some searching, but have not …

Jul 4, 2015 · Usually the parenthesized $\pmod y$ goes at the right of the line, right-justified. So it is a qualifier which tells you which equivalence relation is intended.

Aug 28, 2024 · Then if $a=g^l$ the problem is to find integer $t$ such that $$ (g^t)^k \equiv g^l \pmod n$$ this means $$g^ {kt-l}\equiv 1 \pmod n$$ and this is equivalent to $m |kt-l$.

Aug 6, 2016 · How would you show that if $ac≡bc$ $\\mod m$ and $\\gcd(c,m)=d$, then $a≡b$ $\\mod \\frac{m}{d}$? Any help would be much appreciated!

What integers have order $6 \pmod {31}$? Ask Question Asked 12 years, 3 months ago Modified 12 years, 3 months ago

How can I find solution for $x^3 \\equiv 1 \\pmod p$ ($p$ a prime) efficiently? Trivial root is $x_1 = 1$. I need to find other roots $x_2, x_3$.

Oct 7, 2016 · Now consider the congruence $en\equiv s\pmod {p-1}$, where $e$ should ne considered variable. This congruence has a solution if and only if $\gcd (n,p-1)$ divides $s$.

Proof for: $ (a+b)^ {p} \equiv a^p + b^p \pmod p$ Ask Question Asked 12 years, 11 months ago Modified 5 years, 6 months ago

An integer n is a square modulo p if there exists another integer x such that $n \equiv x^2 \pmod p$. Prove that $x^2 \equiv y^2 \pmod p$ if and only if $x \equiv y \pmod p$ or $x \equiv -y \pmod p$.

Prove that $ (\mathbb {Z}_n , +)$, the integers $\pmod {n}$ under addition, is a group. To show that this is a group, I know I need to show three things (in our text, we do not need to show that addition is …