List questions from modular-arithmetic

Published on 05 Jun 2014 - 2:03

370

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Let $p$ be a prime number such that $p \equiv 3 \pmod 4$. Show that $x^2 \equiv -1 \pmod p$ has no solutions.

Published on 06 Jun 2014 - 18:01

187

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Divisibility of sum of exponents

Published on 06 Jun 2014 - 20:33

208

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Given any integers $a,b,c$ and any prime $p$ not a divisor of $ab$, prove that $ax^2+by^2\equiv c\pmod{p}$ is always solvable.

Published on 07 Jun 2014 - 5:26

80

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The existence of primitive algebraic units modulo 3

Published on 27 Mar 2026 - 2:59

4.8k

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How do you prove that $ n^5$ is congruent to $ n$ mod 10?

Published on 25 Mar 2026 - 23:25

80

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To prove that ${2+i \choose i}\equiv k \mod n$ is not possible that $k=0,1,\ldots,n-1 \forall i\ge 0$ and $i \in \mathbb{Z}$ and $n$ is odd.

Published on 10 Jun 2014 - 13:23

1.5k

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Proof that the repeating block of digits in 1/x is at max x-1?

Published on 10 Jun 2014 - 14:28

1.6k

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Polynomial factorisation on integers modulo n

Published on 30 Mar 2026 - 12:36

388

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Find all solutions for modulo equation

Published on 10 Jun 2014 - 17:29

160

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A question about modular arithmetic

Published on 11 Jun 2014 - 19:13

282

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How do I eliminate mod from an expression?

Published on 12 Jun 2014 - 2:57

24

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contextual system of congruences

Published on 25 Mar 2026 - 23:19

82

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Strange things on WolframAlpha: derivation, modulo and doubling result

Published on 25 Mar 2026 - 14:03

764

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Bound on the degree of a determinant of a polynomial matrix

Published on 01 Apr 2026 - 22:16

List Question

Modulus Implication

Let $p$ be a prime number such that $p \equiv 3 \pmod 4$. Show that $x^2 \equiv -1 \pmod p$ has no solutions.

Divisibility of sum of exponents

Given any integers $a,b,c$ and any prime $p$ not a divisor of $ab$, prove that $ax^2+by^2\equiv c\pmod{p}$ is always solvable.

The existence of primitive algebraic units modulo 3

How do you prove that $ n^5$ is congruent to $ n$ mod 10?

To prove that ${2+i \choose i}\equiv k \mod n$ is not possible that $k=0,1,\ldots,n-1 \forall i\ge 0$ and $i \in \mathbb{Z}$ and $n$ is odd.

Proof that the repeating block of digits in 1/x is at max x-1?

Polynomial factorisation on integers modulo n

Find all solutions for modulo equation

A question about modular arithmetic

How do I eliminate mod from an expression?

contextual system of congruences

Strange things on WolframAlpha: derivation, modulo and doubling result

Bound on the degree of a determinant of a polynomial matrix

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