Question

Can we build a generic linear algebraic machinery to calculate divisibility on decimal numbers?

score 59 · Answer 1 · 2019-11-23 10:58:43

59

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Can we build a generic linear algebraic machinery to calculate divisibility on decimal numbers?

Published on 23 Nov 2019 - 10:58

score 219 · Answer 2 · 2019-11-24 02:18:07

219

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Prove that $x^2+px+p^2$ is a factor $(x+p)^n-x^n-p^n$, if $n$ be odd and not divisible by $3$.

Published on 24 Nov 2019 - 2:18

score 82 · Answer 3 · 2026-03-29 13:23:53

82

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Prove $m\mid \gcd(a_1,\dots,a_k)\text{ implies }\gcd(a_1,\dots,a_k)= m\gcd(\frac{a_1}{m},\dots,\frac{a_k}{m})$

Published on 29 Mar 2026 - 13:23

score 79 · Answer 4 · 2019-11-26 03:25:14

79

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Proving if $4|a+3b$ and $4|b+3a$ then $4|a-b$

Published on 26 Nov 2019 - 3:25

score 400 · Answer 5 · 2019-11-26 21:42:59

400

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Two numbers divisible by the same prime. If concatenated still divisible by the same prime number?

Published on 26 Nov 2019 - 21:42

score 2.2k · Answer 6 · 2026-03-28 11:22:07

2.2k

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Understanding why gcd(a,m) = gcd(b,m) = 1 implies gcd(ab, m) = 1

Published on 28 Mar 2026 - 11:22

score 747 · Answer 7 · 2019-11-30 00:43:24

747

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Prove by mathematical induction that $(3n+1)7^n -1$ is divisible by $9$ for integral $n>0$

Published on 30 Nov 2019 - 0:43

score 848 · Answer 8 · 2019-11-30 13:01:50

848

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Is every prime is the largest prime factor in some prime gap?

Published on 30 Nov 2019 - 13:01

score 74 · Answer 9 · 2026-03-29 14:54:34

74

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Accidental divisibility sequence?

Published on 29 Mar 2026 - 14:54

score 53 · Answer 10 · 2019-12-01 11:55:08

$S= 2^{1} + 22^{11} + 222^{111} \cdots +22222222222^{11111111111}$. Remainder if $S$ is divided by $7?$ Prove that $S$ is not divisible by $5.$

score 74 · Answer 11 · 2026-03-29 05:27:23

74

Views

Prove that numerator of fraction $\sum \limits_{k=1}^{p-2}\frac{k}{(k+1)^2}$ is divisible by $p$ for all prime $p>3$

Published on 29 Mar 2026 - 5:27

score 764 · Answer 12 · 2026-03-29 07:28:46

764

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Suppose that n is an integer such that 5|(n + 2)

Published on 29 Mar 2026 - 7:28

score 148 · Answer 13 · 2026-03-28 11:13:39

148

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if a prime p|LCM[a,b] then p|a or p|b

Published on 28 Mar 2026 - 11:13

score 275 · Answer 14 · 2019-12-04 15:21:44

275

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Prove that numbers of the form 131, 1331, 13331, ... are divisible by 19 when they have length 15+18k

Published on 04 Dec 2019 - 15:21

score 85 · Answer 15 · 2026-03-29 14:55:36

85

Views

Proof Verification - divisibility through induction

Published on 29 Mar 2026 - 14:55

List Question

Can we build a generic linear algebraic machinery to calculate divisibility on decimal numbers?

Prove that $x^2+px+p^2$ is a factor $(x+p)^n-x^n-p^n$, if $n$ be odd and not divisible by $3$.

Prove $m\mid \gcd(a_1,\dots,a_k)\text{ implies }\gcd(a_1,\dots,a_k)= m\gcd(\frac{a_1}{m},\dots,\frac{a_k}{m})$

Proving if $4|a+3b$ and $4|b+3a$ then $4|a-b$

Two numbers divisible by the same prime. If concatenated still divisible by the same prime number?

Understanding why gcd(a,m) = gcd(b,m) = 1 implies gcd(ab, m) = 1

Prove by mathematical induction that $(3n+1)7^n -1$ is divisible by $9$ for integral $n>0$

Is every prime is the largest prime factor in some prime gap?

Accidental divisibility sequence?

$S= 2^{1} + 22^{11} + 222^{111} \cdots +22222222222^{11111111111}$. Remainder if $S$ is divided by $7?$ Prove that $S$ is not divisible by $5.$

Prove that numerator of fraction $\sum \limits_{k=1}^{p-2}\frac{k}{(k+1)^2}$ is divisible by $p$ for all prime $p>3$

Suppose that n is an integer such that 5|(n + 2)

if a prime p|LCM[a,b] then p|a or p|b

Prove that numbers of the form 131, 1331, 13331, ... are divisible by 19 when they have length 15+18k

Proof Verification - divisibility through induction

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