List questions from modular-arithmetic

Published on 25 Mar 2026 - 13:04

335

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For a prime of the form $p=2k+1$, show that if $p\!\!\not|a$ and $a\equiv b^{2}\!\!\mod p$, then $a^k\equiv1\!\!\mod p$.

Published on 30 May 2018 - 0:15

65

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Prime numbers and divisibility related problem

Published on 30 May 2018 - 7:02

26

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Calculate when jobs scheduled with different frequencies will align

Published on 30 May 2018 - 12:45

481

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IMO 2005 No 4. : All integers relatively prime to terms of infinite sequence

Published on 26 Mar 2026 - 11:05

58

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Mod remainders of Biprimes and their factors

Published on 01 Jun 2018 - 9:40

103

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How can I disprove that $13\mid 2^{70}+5^{70}$

Published on 01 Jun 2018 - 17:22

70

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Solving congruences involving addition for CRT

Published on 02 Jun 2018 - 1:18

147

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Without brute force, how can we show that 1729 is the smallest number that can be expressesed as the sum of two cubes in two different ways?

Published on 26 Mar 2026 - 14:34

39

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$\mathbb{Z} / p \mathbb{Z}$ exercise

Published on 02 Jun 2018 - 15:55

41

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continuing congruence equation

Published on 03 Jun 2018 - 10:11

71

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Unable to simplify congruence equation

Published on 03 Jun 2018 - 11:26

78

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Proving bijection of a one way function

Published on 03 Jun 2018 - 12:35

3k

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Show that the square of any odd positive integer is of the type 6q or 6q+ 3 or 6q + 5 where q is some integer

Published on 03 Jun 2018 - 13:00

1.3k

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Number of solutions to the congruence $x^2\equiv 121\pmod {1800}$

Published on 26 Mar 2026 - 1:25

List Question

Solving a^(b^c) using fermats little theorem

For a prime of the form $p=2k+1$, show that if $p\!\!\not|a$ and $a\equiv b^{2}\!\!\mod p$, then $a^k\equiv1\!\!\mod p$.

Prime numbers and divisibility related problem

Calculate when jobs scheduled with different frequencies will align

IMO 2005 No 4. : All integers relatively prime to terms of infinite sequence

Mod remainders of Biprimes and their factors

How can I disprove that $13\mid 2^{70}+5^{70}$

Solving congruences involving addition for CRT

Without brute force, how can we show that 1729 is the smallest number that can be expressesed as the sum of two cubes in two different ways?

$\mathbb{Z} / p \mathbb{Z}$ exercise

continuing congruence equation

Unable to simplify congruence equation

Proving bijection of a one way function

Show that the square of any odd positive integer is of the type 6q or 6q+ 3 or 6q + 5 where q is some integer

Number of solutions to the congruence $x^2\equiv 121\pmod {1800}$

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