Question

Is it true that if $n = 2^k$ for some integer $k\geq 1,$ then $\binom{n}{\frac{n}{2}}$ is an even number?

score 88 · Answer 1 · 2026-03-25 22:27:01

88

Views

Is it true that if $n = 2^k$ for some integer $k\geq 1,$ then $\binom{n}{\frac{n}{2}}$ is an even number?

Published on 25 Mar 2026 - 22:27

score 69 · Answer 2 · 2026-03-28 16:20:41

69

Views

Show that if a prime number $p$ divides an integer $m^2$, then $p$ divides the integer $m$.

Published on 28 Mar 2026 - 16:20

score 60 · Answer 3 · 2026-04-13 12:18:04

60

Views

Closed Form for Solutions of $x^2 \equiv x \text{ mod } 10^n$.

Published on 13 Apr 2026 - 12:18

score 48 · Answer 4 · 2026-04-13 11:27:58

48

Views

Square Root Begins with the Same Digits

Published on 13 Apr 2026 - 11:27

score 40 · Answer 5 · 2026-04-13 14:36:38

40

Views

Is this equality about numbers true?

Published on 13 Apr 2026 - 14:36

score 110 · Answer 6 · 2026-04-03 08:33:30

110

Views

Which subsets of the real numbers can you play Sylver coinage on?

Published on 03 Apr 2026 - 8:33

score 122 · Answer 7 · 2026-04-08 23:12:18

122

Views

Degree $n$ extension of local field splits degree $n$ division algebra

Published on 08 Apr 2026 - 23:12

score 74 · Answer 8 · 2026-04-09 02:02:02

74

Views

Which cycles are possible by repeated summation of the cubes of the digits of a number?

Published on 09 Apr 2026 - 2:02

score 41 · Answer 9 · 2026-04-12 00:40:17

41

Views

A simple modular arithmetic problem

Published on 12 Apr 2026 - 0:40

score 212 · Answer 10 · 2026-04-13 04:37:53

212

Views

show that $\sum \frac {\mu(n)}{10^n}$ is irrational

Published on 13 Apr 2026 - 4:37

score 1.1k · Answer 11 · 2026-03-25 06:21:40

1.1k

Views

Showing $\sum_{n \leq x} \frac{1}{\phi (n)} = C\log x + O(1).$

Published on 25 Mar 2026 - 6:21

score 114 · Answer 12 · 2026-04-12 10:25:33

114

Views

using a sum to give a formula for the nth prime.

Published on 12 Apr 2026 - 10:25

score 553 · Answer 13 · 2018-03-09 00:54:03

Prove that if $p$ is a prime and $a$ and $b$ are nonzero integers such that $a\equiv b$ (mod $p^2-p$), then $a^a \equiv b^b$ (mod $p$)

score 126 · Answer 14 · 2018-03-09 02:19:52

Show that $\sum_{n \leq x} \frac{d(n)}{\log n} = x + 2E \frac{x}{\log x} + O\left( \frac{x}{\log ^2 x} \right).$

score 102 · Answer 15 · 2026-04-08 20:24:43

102

Views

How to evaluate Riemann's Functional Equation

Published on 08 Apr 2026 - 20:24

List Question

Is it true that if $n = 2^k$ for some integer $k\geq 1,$ then $\binom{n}{\frac{n}{2}}$ is an even number?

Show that if a prime number $p$ divides an integer $m^2$, then $p$ divides the integer $m$.

Closed Form for Solutions of $x^2 \equiv x \text{ mod } 10^n$.

Square Root Begins with the Same Digits

Is this equality about numbers true?

Which subsets of the real numbers can you play Sylver coinage on?

Degree $n$ extension of local field splits degree $n$ division algebra

Which cycles are possible by repeated summation of the cubes of the digits of a number?

A simple modular arithmetic problem

show that $\sum \frac {\mu(n)}{10^n}$ is irrational

Showing $\sum_{n \leq x} \frac{1}{\phi (n)} = C\log x + O(1).$

using a sum to give a formula for the nth prime.

Prove that if $p$ is a prime and $a$ and $b$ are nonzero integers such that $a\equiv b$ (mod $p^2-p$), then $a^a \equiv b^b$ (mod $p$)

Show that $\sum_{n \leq x} \frac{d(n)}{\log n} = x + 2E \frac{x}{\log x} + O\left( \frac{x}{\log ^2 x} \right).$

How to evaluate Riemann's Functional Equation

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