List questions from modular-arithmetic

Published on 22 Mar 2026 - 11:53

50

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Please vet proof for : If $a \equiv b \pmod n$ and if $d \mid n$, then $a \equiv b \pmod d$

Published on 19 Jan 2018 - 9:13

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

2.6k

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How to combine congruences?

Published on 19 Mar 2026 - 21:26

27

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Number of solutions of $a \equiv b \pmod m.$

Published on 22 Mar 2026 - 18:34

227

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If $n^{9}=19m+r $ then what is $r\mod19$

Published on 19 Jan 2018 - 22:11

95

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Does this congruence equation system have no solutions?

Published on 24 Mar 2026 - 22:08

890

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Fibonacci numbers mod $p$

Published on 21 Mar 2026 - 10:54

720

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System of two congruence equations

Published on 24 Mar 2026 - 22:01

226

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How do I find all integers that satisfy this condition?

Published on 19 Mar 2026 - 16:52

45

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How do I show these two number theory relationships are the same?

Published on 14 Mar 2026 - 12:30

103

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Quick calculation of modulo with large exponent

Published on 22 Mar 2026 - 11:23

2.1k

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Specific steps in applying the Chinese Remainder Theorem to solve modular problem splitting modulus

Published on 14 Mar 2026 - 0:12

34

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

Published on 24 Mar 2026 - 21:19

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

List Question

Changing modulus in modular arithmetic

Please vet proof for : If $a \equiv b \pmod n$ and if $d \mid n$, then $a \equiv b \pmod d$

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

How to combine congruences?

Number of solutions of $a \equiv b \pmod m.$

If $n^{9}=19m+r $ then what is $r\mod19$

Does this congruence equation system have no solutions?

Fibonacci numbers mod $p$

System of two congruence equations

How do I find all integers that satisfy this condition?

How do I show these two number theory relationships are the same?

Quick calculation of modulo with large exponent

Specific steps in applying the Chinese Remainder Theorem to solve modular problem splitting modulus

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 $b$.

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