List questions from congruence-relations

193

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Proof congruence identity modulo $p$: $2^2\cdot4^2\cdot\dots\cdot(p-3)^2\cdot(p-1)^2 \equiv (-1)^{\frac{1}{2}(p+1)}\mod{p}$

Published on 24 Mar 2026 - 15:30

33

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Proof verification: $a+b\equiv b+a \;\; (mod\;\;n)$ and $ab\equiv ba \;\; (mod\;\;n)$.

Published on 15 Mar 2026 - 4:16

1.8k

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Proof verification: $\gcd(a,n)=1$ iff $ab\equiv 1\pmod{n}$ for some integer $b$.

Published on 22 Mar 2026 - 3:10

578

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Does congruence transformation preserve definiteness of a nonsymmetric matrix?

Published on 20 Mar 2026 - 7:21

366

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Why linear congruential generator is called random number generator?

Published on 21 Mar 2026 - 16:11

55

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Prove co-prime exist

Published on 20 Mar 2026 - 9:36

100

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presentation of amalgamated sum as a quotient of the direct sum

Published on 22 Mar 2026 - 15:40

46

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notation in congruence relation

Published on 22 Mar 2026 - 14:37

50

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Why do these 2 congruences imply the following?

Published on 23 Mar 2026 - 4:55

72

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Is there any way to prove that if $4y=4x+13k$ then $y=x+13l$?

Published on 23 Mar 2026 - 1:06

55

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Congruence relation

Published on 23 Mar 2026 - 5:24

345

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For what values of n is $f(x) = x^3 mod(n)$ a bijection from $X={(0,1,2,...,n-1)}$ to itself.

Published on 16 Mar 2026 - 21:56

364

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Chinese Remainder Theorem, Miller-Rabin Primality test, and more...

Published on 16 Mar 2026 - 23:50

61

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Lucas Reciprocity Laws

Published on 23 Mar 2026 - 0:07

159

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$a^2 + b^2 \equiv 0 \pmod{p}$ and $p \nmid a, b$

Published on 21 Mar 2026 - 22:19

List Question

Proof congruence identity modulo $p$: $2^2\cdot4^2\cdot\dots\cdot(p-3)^2\cdot(p-1)^2 \equiv (-1)^{\frac{1}{2}(p+1)}\mod{p}$

Proof verification: $a+b\equiv b+a \;\; (mod\;\;n)$ and $ab\equiv ba \;\; (mod\;\;n)$.

Proof verification: $\gcd(a,n)=1$ iff $ab\equiv 1\pmod{n}$ for some integer $b$.

Does congruence transformation preserve definiteness of a nonsymmetric matrix?

Why linear congruential generator is called random number generator?

Prove co-prime exist

presentation of amalgamated sum as a quotient of the direct sum

notation in congruence relation

Why do these 2 congruences imply the following?

Is there any way to prove that if $4y=4x+13k$ then $y=x+13l$?

Congruence relation

For what values of n is $f(x) = x^3 mod(n)$ a bijection from $X={(0,1,2,...,n-1)}$ to itself.

Chinese Remainder Theorem, Miller-Rabin Primality test, and more...

Lucas Reciprocity Laws

$a^2 + b^2 \equiv 0 \pmod{p}$ and $p \nmid a, b$

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