Question

How many solutions does $x \equiv x^{-1} \pmod n$ have?

score 97 · Answer 1 · 2026-04-14 08:29:15

How many solutions does $x \equiv x^{-1} \pmod n$ have?

Published on 14 Apr 2026 - 8:29

score 43 · Answer 2 · 2026-04-17 04:06:56

If $t^p-(r^p+s^p) \equiv 0 (\mod p)$ implies $t-(r+s)=pq$, do other solutions exist for relatively prime $r$, $s$ and $t$?

score 515 · Answer 3 · 2026-04-10 03:10:36

515

Views

Distinct prime number solution of an equation

Published on 10 Apr 2026 - 3:10

score 152 · Answer 4 · 2026-05-11 08:41:59

152

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For natural $n$, let $1=d_1<d_2<\cdots<d_k=n$ be the positive divisors of $n$. Find the smallest $n$ such that $2n=d_5^2+d_6^2-1$

Published on 11 May 2026 - 8:41

score 126 · Answer 5 · 2026-04-29 02:31:00

126

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Question pertaining to perfect powers in sums of consecutive integers

Published on 29 Apr 2026 - 2:31

score 153 · Answer 6 · 2026-04-15 06:25:02

153

Views

Initially there are m balls in one bag, and n in the other, where m, n > 0. Two different operations are allowed:

Published on 15 Apr 2026 - 6:25

score 261 · Answer 7 · 2026-04-14 04:05:03

261

Views

Cubic Diophantine Equation of Two Variables

Published on 14 Apr 2026 - 4:05

score 100 · Answer 8 · 2026-04-16 01:12:43

Find all positive triples of positive integers a, b, c so that $\frac {a+1}{b}$ , $\frac {b+1}{c}$, $\frac {c+1}{a}$ are also integers.

score 63 · Answer 9 · 2026-05-04 04:42:57

63

Views

Is it true that if $x \ge 2000$, then the least common multiple of $\{1,2,3,\dots,x\}$ is greater than $2.499^x$

Published on 04 May 2026 - 4:42

score 67 · Answer 10 · 2026-05-10 15:30:06

67

Views

Probability of $f(n) - \varphi(n)$ to be an even number.

Published on 10 May 2026 - 15:30

score 58 · Answer 11 · 2026-04-24 14:38:13

58

Views

Is it true that $\sum_{k=0}^{n}k\cdot \left(\begin{array}{l}{n}\\{k}\end{array}\right)=O\left(2 ^ {n\log _{3}n}\right)?$

Published on 24 Apr 2026 - 14:38

score 145 · Answer 12 · 2026-05-10 15:09:55

145

Views

What is the largest known twin-prime of the form $2^a\cdot 3^b\pm 1$?

Published on 10 May 2026 - 15:09

score 497 · Answer 13 · 2026-03-26 01:23:37

497

Views

When extending the natural numbers to the integers when is it legal to set a natural number equal to an integer.

Published on 26 Mar 2026 - 1:23

score 119 · Answer 14 · 2026-04-09 05:51:24

119

Views

Let $n\in \mathbb{N}, n > 1$ Show that some numbers are coprimes.

Published on 09 Apr 2026 - 5:51

score 87 · Answer 15 · 2026-05-10 16:17:35

87

Views

Why is it impossible to invert the analytic continuation of a Dirichlet series?

Published on 10 May 2026 - 16:17

List Question

How many solutions does $x \equiv x^{-1} \pmod n$ have?

If $t^p-(r^p+s^p) \equiv 0 (\mod p)$ implies $t-(r+s)=pq$, do other solutions exist for relatively prime $r$, $s$ and $t$?

Distinct prime number solution of an equation

For natural $n$, let $1=d_1<d_2<\cdots<d_k=n$ be the positive divisors of $n$. Find the smallest $n$ such that $2n=d_5^2+d_6^2-1$

Question pertaining to perfect powers in sums of consecutive integers

Initially there are m balls in one bag, and n in the other, where m, n > 0. Two different operations are allowed:

Cubic Diophantine Equation of Two Variables

Find all positive triples of positive integers a, b, c so that $\frac {a+1}{b}$ , $\frac {b+1}{c}$, $\frac {c+1}{a}$ are also integers.

Is it true that if $x \ge 2000$, then the least common multiple of $\{1,2,3,\dots,x\}$ is greater than $2.499^x$

Probability of $f(n) - \varphi(n)$ to be an even number.

Is it true that $\sum_{k=0}^{n}k\cdot \left(\begin{array}{l}{n}\\{k}\end{array}\right)=O\left(2 ^ {n\log _{3}n}\right)?$

What is the largest known twin-prime of the form $2^a\cdot 3^b\pm 1$?

When extending the natural numbers to the integers when is it legal to set a natural number equal to an integer.

Let $n\in \mathbb{N}, n > 1$ Show that some numbers are coprimes.

Why is it impossible to invert the analytic continuation of a Dirichlet series?

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