New posts in congruences

Prove that a number is divisible by 3 iff the sum of its digits is divisible by 3

Proof by contradiction Let $n \in \mathbb{N}$. Any odd prime factor $p$ of $n^2 +1$ has the form $p = 4k+1$ for some integer $k \geq 0$.

elementary-number-theory congruences

Show that for every prime $p$, there is an integer $n$ such that $2^{n}+3^{n}+6^{n}-1$ is divisible by $p$.

number-theory elementary-number-theory prime-numbers modular-arithmetic congruences

If $p$ is prime and $p$ $\equiv$ $1$ (mod 4), then the congruence $x^2$ $\equiv$ $-1$ (mod $p$) has two incongruent solutions...

elementary-number-theory prime-numbers congruences

Flaw or no flaw in MS Excel's RNG?

proof-verification congruences random math-software chinese-remainder-theorem

Modular congruence, splitting a modulo

modular-arithmetic congruences

Number Theory: Complete set of residues modulo $n$

elementary-number-theory modular-arithmetic congruences

I finally understand simple congruences. Now how to solve a quadratic congruence?

number-theory elementary-number-theory modular-arithmetic congruences

Proof that there are infinitely many primes congruent to 3 modulo 4

elementary-number-theory prime-numbers proof-writing congruences

Number Theory: Solutions of $ax^2+by^2\equiv1 \pmod p$

number-theory elementary-number-theory congruences quadratic-reciprocity

Solve congruence: $45x \equiv 15 \pmod{78}$ (What am I doing wrong?)

elementary-number-theory modular-arithmetic congruences

Proof Using Wilson's Theorem

number-theory prime-numbers factorial congruences

Is the number $333{,}333{,}333{,}333{,}333{,}333{,}333{,}333{,}334$ a perfect square?

elementary-number-theory discrete-mathematics modular-arithmetic divisibility congruences

Solving linear congruence $2x + 11 \equiv 7 \pmod 3$

modular-arithmetic arithmetic congruences

Proving $n^{17} \equiv n \;(\text{mod}\; 510)$

Prove that if $n$ is not divisible by $5$, then $n^4 \equiv 1 \pmod{5}$

elementary-number-theory congruences

Show for prime numbers of the form $p=4n+1$, $x=(2n)!$ solves the congruence $x^2\equiv-1 \pmod p$. $p$ is therefore not a gaussian prime.

elementary-number-theory prime-numbers congruences

Why do we use "congruent to" instead of equal to?

notation modular-arithmetic congruences

What is the difference between Hensel lifting and the Newton-Raphson method?

elementary-number-theory numerical-methods congruences

Solving the congruence $x^2 \equiv 4 \mod 105$. Is there an alternative to using Chinese Remainder Theorem multiple times?

elementary-number-theory modular-arithmetic congruences cryptography chinese-remainder-theorem