Question

Is $n^2+3n+6$ divisible by 25, where $n$ is a integer?

score 86 · Answer 1 · 2019-03-11 09:53:24

86

Views

Is $n^2+3n+6$ divisible by 25, where $n$ is a integer?

Published on 11 Mar 2019 - 9:53

score 337 · Answer 2 · 2019-03-12 05:55:28

337

Views

Modular Arithmetic with Negative Exponents

Published on 12 Mar 2019 - 5:55

score 263 · Answer 3 · 2019-03-12 10:42:29

263

Views

A006517: Numbers with $n\mid 2^n+2$

Published on 12 Mar 2019 - 10:42

score 22 · Answer 4 · 2019-03-13 01:51:44

22

Views

For positive integers prove that $a\Big|bc \implies a\Big|b \lor a\Big|c$

Published on 13 Mar 2019 - 1:51

score 147 · Answer 5 · 2019-03-13 07:10:19

147

Views

Exercise on polynomial and GCD

Published on 13 Mar 2019 - 7:10

score 136 · Answer 6 · 2019-03-13 10:53:07

136

Views

How to elegantly find the remainder of $en$ divided by $n+1+\frac{n-1}{d}$

Published on 13 Mar 2019 - 10:53

score 87 · Answer 7 · 2019-03-13 11:13:47

87

Views

Is there a positive integer $n$ where $14$ divide $30^n$? Explain why.

Published on 13 Mar 2019 - 11:13

score 691 · Answer 8 · 2019-03-13 13:01:32

691

Views

How many five digit numbers formed from digits $1,2,3,4,5$ (used exactly once) are divisible by $12$?

Published on 13 Mar 2019 - 13:01

score 62 · Answer 9 · 2019-03-14 19:18:23

62

Views

Testing polynomial divisibility by evaluation at specific points

Published on 14 Mar 2019 - 19:18

score 169 · Answer 10 · 2019-03-15 19:26:02

169

Views

If $d$ divides $2n$ and $d$ doesn't divide $n$, then $d$ is even

Published on 15 Mar 2019 - 19:26

score 98 · Answer 11 · 2026-03-26 19:38:07

98

Views

Prove that the sum is not an integer

Published on 26 Mar 2026 - 19:38

score 206 · Answer 12 · 2026-03-25 15:12:10

206

Views

What are the necessary conditions for a polynomial Q(X) such that the roots of Q(X) - X are equal to the real roots of a polynomial P?

Published on 25 Mar 2026 - 15:12

score 585 · Answer 13 · 2019-03-19 03:54:10

Prove that there exist $135$ consecutive positive integers so that the $n$th least is divisible by a perfect $n$th power greater than $1$

score 149 · Answer 14 · 2026-03-26 23:10:51

149

Views

Suppose that $T$ is the smallest positive integer satisfying $m^{T}\equiv \pmod {pq}$. Prove that $T\mid(p-1)(q-1)$.

Published on 26 Mar 2026 - 23:10

score 55 · Answer 15 · 2026-03-25 11:10:00

55

Views

Number System Divisibility by 7

Published on 25 Mar 2026 - 11:10

List Question

Is $n^2+3n+6$ divisible by 25, where $n$ is a integer?

Modular Arithmetic with Negative Exponents

A006517: Numbers with $n\mid 2^n+2$

For positive integers prove that $a\Big|bc \implies a\Big|b \lor a\Big|c$

Exercise on polynomial and GCD

How to elegantly find the remainder of $en$ divided by $n+1+\frac{n-1}{d}$

Is there a positive integer $n$ where $14$ divide $30^n$? Explain why.

How many five digit numbers formed from digits $1,2,3,4,5$ (used exactly once) are divisible by $12$?

Testing polynomial divisibility by evaluation at specific points

If $d$ divides $2n$ and $d$ doesn't divide $n$, then $d$ is even

Prove that the sum is not an integer

What are the necessary conditions for a polynomial Q(X) such that the roots of Q(X) - X are equal to the real roots of a polynomial P?

Prove that there exist $135$ consecutive positive integers so that the $n$th least is divisible by a perfect $n$th power greater than $1$

Suppose that $T$ is the smallest positive integer satisfying $m^{T}\equiv \pmod {pq}$. Prove that $T\mid(p-1)(q-1)$.

Number System Divisibility by 7

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