List questions from modular-arithmetic

Published on 25 Mar 2026 - 15:49

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Affine cypher. Find function and plaintext

Published on 26 Mar 2026 - 3:10

994

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Show that $61!+1$ is divisible by $71$

Published on 06 Feb 2019 - 5:41

427

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Find the remainder when $99!+99$ is divided by $100$

Published on 06 Feb 2019 - 6:25

135

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Calculate $1434661\cdot 3785648743-10020304\cdot 54300201$

Published on 06 Feb 2019 - 6:29

106

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Solve in $\mathbb N$: $ 2^x\equiv 1 \bmod{x}$

Published on 28 Mar 2026 - 15:18

1.3k

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Find the multiplicative inverse of $(5^{14})$, mod $17$. Give your answer as a number in the set {$0, 1, 2,...,16$}. Do not use a calculator.

Published on 06 Feb 2019 - 16:01

84

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Find the remainder when $2^{837259739}+ 3^{23456}$ is divided by $31$

Published on 06 Feb 2019 - 18:11

52

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Modular Exponentiation Speedup

Published on 26 Mar 2026 - 17:29

219

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Determine if there is a solution to the congruence $x^6+5x^2 \equiv 2\mod 7$

Published on 06 Feb 2019 - 21:10

99

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prove or disprove: If $c > 0$ and $a < b < c $ , then $a \not \equiv b$ mod $c$

Published on 06 Feb 2019 - 21:32

68

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Use WOP to prove that for integers $a, m > 0$ there are integers $q, r \ge 0$, with $r \in \{0,1,2,\dots, m-1\}$ such that $a=qm+r$

Published on 06 Feb 2019 - 22:30

59

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How to prove if $x \in\mathbb N$ and $y \in\mathbb N$, then $(x\mod y) \in\mathbb N$?

Published on 07 Feb 2019 - 0:30

346

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Solution to a system of quadratic congruences.

Published on 25 Mar 2026 - 9:38

385

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How to write modular notation?

Published on 07 Feb 2019 - 3:22

List Question

Find $21^{1234}\pmod{100}\equiv \ ?$

Affine cypher. Find function and plaintext

Show that $61!+1$ is divisible by $71$

Find the remainder when $99!+99$ is divided by $100$

Calculate $1434661\cdot 3785648743-10020304\cdot 54300201$

Solve in $\mathbb N$: $ 2^x\equiv 1 \bmod{x}$

Find the multiplicative inverse of $(5^{14})$, mod $17$. Give your answer as a number in the set {$0, 1, 2,...,16$}. Do not use a calculator.

Find the remainder when $2^{837259739}+ 3^{23456}$ is divided by $31$

Modular Exponentiation Speedup

Determine if there is a solution to the congruence $x^6+5x^2 \equiv 2\mod 7$

prove or disprove: If $c > 0$ and $a < b < c $ , then $a \not \equiv b$ mod $c$

Use WOP to prove that for integers $a, m > 0$ there are integers $q, r \ge 0$, with $r \in \{0,1,2,\dots, m-1\}$ such that $a=qm+r$

How to prove if $x \in\mathbb N$ and $y \in\mathbb N$, then $(x\mod y) \in\mathbb N$?

Solution to a system of quadratic congruences.

How to write modular notation?

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