List questions from congruences

Published on 25 Mar 2026 - 18:57

89

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Prove that $x^2 \not \equiv 3$ (mod 9)

Published on 25 Mar 2026 - 20:34

240

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Solve the system of linear congruences below by finding all $x$ that satisfy it.

Published on 03 Nov 2017 - 16:45

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Solving system of congruences where $m$'s are not coprime

Published on 03 Nov 2017 - 22:24

78

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Proof involving coprime integers with the same quadratic residue

Published on 29 Mar 2026 - 17:24

186

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$n^k \equiv n \pmod 5 $ for all $ n\in \mathbb Z $ iff $k \equiv 1\pmod 4 $

Published on 06 Nov 2017 - 8:05

90

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Prove that, for any $x$, $x^2 \equiv 3 \pmod{9}$ cannot be true

Published on 06 Nov 2017 - 8:12

100

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Smallest number ended in 6 that changin a digit of place becomes four times itself

Published on 07 Nov 2017 - 20:36

71

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A set of n equations that equal each other

Published on 07 Nov 2017 - 22:48

900

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prove that 15 divides $n^7+2n^5+4n^3+8n$ for any integer n

Published on 09 Nov 2017 - 8:08

45

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Show whether the function $\phi(x)=21x \bmod 36$ is one-to-one and/or onto

Published on 02 Apr 2026 - 12:24

197

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Prove that n is a prime number if and only if $(n−2)! \equiv 1 \pmod n$.

Published on 09 Nov 2017 - 20:44

196

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Calculate remainder when $2^{403}$ is divided by 22

Published on 09 Nov 2017 - 21:15

295

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modular exponentiation by hand for large numbers.

Published on 10 Nov 2017 - 2:02

343

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Unit's digit of exponential factorial

Published on 10 Nov 2017 - 16:35

List Question

Prove if $ x^{11}\equiv 21$ (mod $59$) then $x^{9}\equiv 35$ (mod $59$)

Prove that $x^2 \not \equiv 3$ (mod 9)

Solve the system of linear congruences below by finding all $x$ that satisfy it.

Solving system of congruences where $m$'s are not coprime

Proof involving coprime integers with the same quadratic residue

$n^k \equiv n \pmod 5 $ for all $ n\in \mathbb Z $ iff $k \equiv 1\pmod 4 $

Prove that, for any $x$, $x^2 \equiv 3 \pmod{9}$ cannot be true

Smallest number ended in 6 that changin a digit of place becomes four times itself

A set of n equations that equal each other

prove that 15 divides $n^7+2n^5+4n^3+8n$ for any integer n

Show whether the function $\phi(x)=21x \bmod 36$ is one-to-one and/or onto

Prove that n is a prime number if and only if $(n−2)! \equiv 1 \pmod n$.

Calculate remainder when $2^{403}$ is divided by 22

modular exponentiation by hand for large numbers.

Unit's digit of exponential factorial

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