Question

Proof: For any prime number $p$, there must be integer $a$, $b$, $c$, $d$ such that $x^4+1 \equiv (x^2+ax+b)(x^2+cx+d)\ (mod\ p)$.

score 81 · Answer 1 · 2026-04-17 09:00:26

81

Views

Proof: For any prime number $p$, there must be integer $a$, $b$, $c$, $d$ such that $x^4+1 \equiv (x^2+ax+b)(x^2+cx+d)\ (mod\ p)$.

Published on 17 Apr 2026 - 9:00

score 88 · Answer 2 · 2026-04-16 07:43:22

88

Views

Is it necessary for a number of the form $4k^2+1$ to have at least one prime factor of the form $4n+1$?

Published on 16 Apr 2026 - 7:43

score 56 · Answer 3 · 2026-05-14 22:43:41

56

Views

If any alternative numbering systems exist that simplify thinking about arbitrary numbers

Published on 14 May 2026 - 22:43

score 28 · Answer 4 · 2026-04-13 15:02:43

28

Views

Given an input / output and set of permitted operations find a formula

Published on 13 Apr 2026 - 15:02

score 116 · Answer 5 · 2026-04-13 22:03:02

116

Views

Multiplicative order of $a\bmod c^{k+1}$

Published on 13 Apr 2026 - 22:03

score 61 · Answer 6 · 2026-04-16 16:08:02

61

Views

Convergence of a special sequence.

Published on 16 Apr 2026 - 16:08

score 147 · Answer 7 · 2026-04-11 03:03:38

147

Views

Given a finite group, does this equation involving group's order, a partition of it and centralizers' orders hold?_Attempt#2

Published on 11 Apr 2026 - 3:03

score 695 · Answer 8 · 2026-05-16 04:11:04

695

Views

What will be the minimum value of $abab$ (a 4 digit number) for its maximum number of factors?

Published on 16 May 2026 - 4:11

score 43 · Answer 9 · 2026-04-14 15:03:24

43

Views

if $a$ is an algebraic integer and $m\in \mathbb{Z}$ then $a+m$ is an algebraic integer.

Published on 14 Apr 2026 - 15:03

score 168 · Answer 10 · 2026-05-16 20:48:39

168

Views

How many digits are there in a number($x$) that contains only $3$,$4$,$5$ & $6$ when the sum of digits of $x$ and $2x$ is 900?

Published on 16 May 2026 - 20:48

score 111 · Answer 11 · 2026-04-14 04:29:27

111

Views

If $x^2+ax+b+1=0$ ($a,b\in\mathbb{Z}$) has integral roots, prove that $a^2+b^2$ is composite.

Published on 14 Apr 2026 - 4:29

score 206 · Answer 12 · 2026-05-14 06:12:05

206

Views

Cocompact & discrete lattice

Published on 14 May 2026 - 6:12

score 1.2k · Answer 13 · 2026-05-13 04:31:23

1.2k

Views

Expression for the inverse of Euler's totient function $\phi^{-1}$

Published on 13 May 2026 - 4:31

score 76 · Answer 14 · 2026-04-15 05:04:58

76

Views

Minimum number of equidistant elements in finite integer sequence

Published on 15 Apr 2026 - 5:04

score 98 · Answer 15 · 2026-04-16 20:45:05

Primes and the function $\displaystyle\prod_{\substack{p \in \mathbb{P}}} \Big( {\normalsize 1-\left(\frac{z-1}{p-1}\right)^2}\Big)$

List Question

Proof: For any prime number $p$, there must be integer $a$, $b$, $c$, $d$ such that $x^4+1 \equiv (x^2+ax+b)(x^2+cx+d)\ (mod\ p)$.

Is it necessary for a number of the form $4k^2+1$ to have at least one prime factor of the form $4n+1$?

If any alternative numbering systems exist that simplify thinking about arbitrary numbers

Given an input / output and set of permitted operations find a formula

Multiplicative order of $a\bmod c^{k+1}$

Convergence of a special sequence.

Given a finite group, does this equation involving group's order, a partition of it and centralizers' orders hold?_Attempt#2

What will be the minimum value of $abab$ (a 4 digit number) for its maximum number of factors?

if $a$ is an algebraic integer and $m\in \mathbb{Z}$ then $a+m$ is an algebraic integer.

How many digits are there in a number($x$) that contains only $3$,$4$,$5$ & $6$ when the sum of digits of $x$ and $2x$ is 900?

If $x^2+ax+b+1=0$ ($a,b\in\mathbb{Z}$) has integral roots, prove that $a^2+b^2$ is composite.

Cocompact & discrete lattice

Expression for the inverse of Euler's totient function $\phi^{-1}$

Minimum number of equidistant elements in finite integer sequence

Primes and the function $\displaystyle\prod_{\substack{p \in \mathbb{P}}} \Big( {\normalsize 1-\left(\frac{z-1}{p-1}\right)^2}\Big)$

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