Question

How many non-empty subsets of $1,2,3,\cdots,p-2,p-1$ have a sum which is divisible by $p$ that $p$ is an odd prime?

score 733 · Answer 1 · 2019-11-15 02:41:29

733

Views

How many non-empty subsets of $1,2,3,\cdots,p-2,p-1$ have a sum which is divisible by $p$ that $p$ is an odd prime?

Published on 15 Nov 2019 - 2:41

score 87 · Answer 2 · 2019-11-15 05:06:03

87

Views

Divisibility Induction $17|18^{(5n+1)}+13^{(4n+1)}+3$

Published on 15 Nov 2019 - 5:06

score 109 · Answer 3 · 2019-11-15 12:19:20

109

Views

$(-4339 \cdot 8559) \text{ mod } 43$ without calculator

Published on 15 Nov 2019 - 12:19

score 229 · Answer 4 · 2026-03-29 13:22:57

229

Views

Prove that $(an+bm)!$ is divisible by $m!.n!$

Published on 29 Mar 2026 - 13:22

score 25 · Answer 5 · 2026-03-25 23:39:41

25

Views

An inequality involving common polynomial divisors of maximal degree

Published on 25 Mar 2026 - 23:39

score 35 · Answer 6 · 2019-11-17 19:05:36

35

Views

Proving If A then B ...

Published on 17 Nov 2019 - 19:05

score 176 · Answer 7 · 2019-11-18 21:36:38

176

Views

prove that $5^{2n+1} - 3^{2n+1} - 2^{2n+1}$ is divisible by 30 for all integers n ≥ 0.

Published on 18 Nov 2019 - 21:36

score 99 · Answer 8 · 2026-03-28 11:33:37

99

Views

Prove that if $2| U_n$ then $4| (U_{n+1}^2 -U_{n-1}^2)$

Published on 28 Mar 2026 - 11:33

score 32 · Answer 9 · 2019-11-19 07:24:19

32

Views

optimal number of divisors for powers of 2

Published on 19 Nov 2019 - 7:24

score 41 · Answer 10 · 2019-11-19 19:19:17

41

Views

$a+b+c=9k,\,a≠b≠c,\,a,b,c∈N \, and\, a,b,c<10$

Published on 19 Nov 2019 - 19:19

score 63 · Answer 11 · 2019-11-20 17:14:08

63

Views

Division with remainder in $\mathbb R$

Published on 20 Nov 2019 - 17:14

score 772 · Answer 12 · 2019-11-20 17:17:45

772

Views

On the coefficients of $(x-1)...(x-(p-1))$

Published on 20 Nov 2019 - 17:17

score 71 · Answer 13 · 2019-11-22 15:23:04

71

Views

Discrete math proof methods: Does $m\mid a\cdot b\cdot c$ imply $m\mid a$ or $m\mid b$ or $m\mid c$?

Published on 22 Nov 2019 - 15:23

score 77 · Answer 14 · 2019-11-22 22:40:59

77

Views

Show that $ 7\mid (a + 3) $

Published on 22 Nov 2019 - 22:40

score 241 · Answer 15 · 2026-04-01 00:55:22

241

Views

Solutions $a,b,c \mid 1+a+b+c $ over positive integers algebraically (avoiding brute force)?

Published on 01 Apr 2026 - 0:55

List Question

How many non-empty subsets of $1,2,3,\cdots,p-2,p-1$ have a sum which is divisible by $p$ that $p$ is an odd prime?

Divisibility Induction $17|18^{(5n+1)}+13^{(4n+1)}+3$

$(-4339 \cdot 8559) \text{ mod } 43$ without calculator

Prove that $(an+bm)!$ is divisible by $m!.n!$

An inequality involving common polynomial divisors of maximal degree

Proving If A then B ...

prove that $5^{2n+1} - 3^{2n+1} - 2^{2n+1}$ is divisible by 30 for all integers n ≥ 0.

Prove that if $2| U_n$ then $4| (U_{n+1}^2 -U_{n-1}^2)$

optimal number of divisors for powers of 2

$a+b+c=9k,\,a≠b≠c,\,a,b,c∈N \, and\, a,b,c<10$

Division with remainder in $\mathbb R$

On the coefficients of $(x-1)...(x-(p-1))$

Discrete math proof methods: Does $m\mid a\cdot b\cdot c$ imply $m\mid a$ or $m\mid b$ or $m\mid c$?

Show that $ 7\mid (a + 3) $

Solutions $a,b,c \mid 1+a+b+c $ over positive integers algebraically (avoiding brute force)?

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