List questions from modular-arithmetic

Published on 19 Jun 2019 - 6:06

46

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$\forall p \ge 11 \quad \exists n \in \{1,2,\dots,9\}$ such that $n$ and $n+1$ are quadratic residues mod p

Published on 26 Mar 2026 - 14:34

346

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Solving a congruence with Chinese Remainder Theorem

Published on 25 Mar 2026 - 18:47

67

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How to calculate 'n' given basic operations like '(n + x) mod p = r' where 'x', 'p', and 'r' are known?

Published on 29 Mar 2026 - 17:25

745

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Why does 3x ≡ -29 (mod 5) equal to 3x ≡ 1 (mod 5)

Published on 19 Jun 2019 - 13:50

1.2k

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Solutions of $x^2 \equiv 1 \pmod N$

Published on 26 Mar 2026 - 14:43

163

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If $x^3$ is a square, is $x$ a square?

Published on 29 Mar 2026 - 10:47

251

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What is the motivation behind defining congruence / residue classes?

Published on 19 Jun 2019 - 17:22

204

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Solutions to $a^2\equiv 1\mod 2^k$

Published on 19 Jun 2019 - 18:18

87

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Modular Arithmetic: Congruence System

Published on 19 Jun 2019 - 18:45

239

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Computing $\sum_{k=1}^n (a^k \bmod m)$

Published on 26 Mar 2026 - 17:43

421

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Solutions mod p of the equation $x^4-17=2y^2$

Published on 28 Mar 2026 - 16:14

490

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Collatz conjecture, Tao-Collatz remainder and mod n.

Published on 25 Mar 2026 - 12:48

139

Views

Sequence of positive integers $n$ such that $n^2+n+1$ divides $4^n+2^n+1$ and $n$ is not power two

Published on 20 Jun 2019 - 14:07

371

Views

Show that a following equation has no solution in integers: $x^3-x+9=5y^2$

Published on 26 Mar 2026 - 21:26

List Question

Find a non-trivial polynomial which has all integers as zeros modulo $p$

$\forall p \ge 11 \quad \exists n \in \{1,2,\dots,9\}$ such that $n$ and $n+1$ are quadratic residues mod p

Solving a congruence with Chinese Remainder Theorem

How to calculate 'n' given basic operations like '(n + x) mod p = r' where 'x', 'p', and 'r' are known?

Why does 3x ≡ -29 (mod 5) equal to 3x ≡ 1 (mod 5)

Solutions of $x^2 \equiv 1 \pmod N$

If $x^3$ is a square, is $x$ a square?

What is the motivation behind defining congruence / residue classes?

Solutions to $a^2\equiv 1\mod 2^k$

Modular Arithmetic: Congruence System

Computing $\sum_{k=1}^n (a^k \bmod m)$

Solutions mod p of the equation $x^4-17=2y^2$

Collatz conjecture, Tao-Collatz remainder and mod n.

Sequence of positive integers $n$ such that $n^2+n+1$ divides $4^n+2^n+1$ and $n$ is not power two

Show that a following equation has no solution in integers: $x^3-x+9=5y^2$

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