List questions from congruences

Published on 22 Mar 2026 - 2:40

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Proving that $45$ is composite using Fermat's Little Theorem

Published on 11 Jun 2015 - 6:57

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Show that $(M^{e})^d \equiv M$ (mod n).

Published on 29 Mar 2026 - 5:42

115

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Find minimal $x\in\Bbb N$ that solves the linear congruence

Published on 13 Jun 2015 - 14:26

148

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Show that $10^{n(p-1)}\equiv 1\pmod{\! 9p}$ for $p\ge 7$

Published on 29 Mar 2026 - 5:50

352

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Unknown random number generator

Published on 15 Jun 2015 - 10:41

97

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Abstract Algebra - Congruence Class Roots

Published on 16 Jun 2015 - 8:08

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Equivalence of congruences - why are these congruences equivalent?

Published on 16 Jun 2015 - 22:27

70

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What's the remainder when $100!+5400$ is divided by $124$?

Published on 17 Jun 2015 - 6:19

74

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Solving a quadratic relation mod $13$

Published on 17 Jun 2015 - 10:55

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Solve $7^x \equiv 6 \pmod{17}$ given 3 is a primitive root $\bmod 17$

Published on 29 Mar 2026 - 8:18

432

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$\binom{2p-1}{p-1}\equiv 1\pmod{\! p^2}$ implies $\binom{ap}{bp}\equiv\binom{a}{b}\pmod{\! p^2}$; where $p>3$ is a prime?

Published on 20 Jun 2015 - 2:05

63

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Solving for solutions to a congruence

Published on 20 Jun 2015 - 3:47

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Show that the number of solutions of $x^2 \equiv 1 \pmod n$ is 2

Published on 29 Mar 2026 - 8:16

338

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Using modular arithmetic to evaluate a modulo operation

Published on 20 Jun 2015 - 15:09

List Question

Understanding the following lemma

Proving that $45$ is composite using Fermat's Little Theorem

Show that $(M^{e})^d \equiv M$ (mod n).

Find minimal $x\in\Bbb N$ that solves the linear congruence

Show that $10^{n(p-1)}\equiv 1\pmod{\! 9p}$ for $p\ge 7$

Unknown random number generator

Abstract Algebra - Congruence Class Roots

Equivalence of congruences - why are these congruences equivalent?

What's the remainder when $100!+5400$ is divided by $124$?

Solving a quadratic relation mod $13$

Solve $7^x \equiv 6 \pmod{17}$ given 3 is a primitive root $\bmod 17$

$\binom{2p-1}{p-1}\equiv 1\pmod{\! p^2}$ implies $\binom{ap}{bp}\equiv\binom{a}{b}\pmod{\! p^2}$; where $p>3$ is a prime?

Solving for solutions to a congruence

Show that the number of solutions of $x^2 \equiv 1 \pmod n$ is 2

Using modular arithmetic to evaluate a modulo operation

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