Question

Prove that $(n-2m)x^n-nx^{n-m}+nx^m-(n-2m)$ is divisble by $(x-1)^3$

score 110 · Answer 1 · 2018-05-14 15:22:21

110

Views

Prove that $(n-2m)x^n-nx^{n-m}+nx^m-(n-2m)$ is divisble by $(x-1)^3$

Published on 14 May 2018 - 15:22

score 582 · Answer 2 · 2018-05-14 17:27:02

582

Views

How to find out if a polynomial has multiple roots?

Published on 14 May 2018 - 17:27

score 73 · Answer 3 · 2018-05-14 18:31:08

73

Views

Checking whether $4a2b$ is can be divided by $36$

Published on 14 May 2018 - 18:31

score 12.1k · Answer 4 · 2026-03-25 11:13:24

12.1k

Views

How to get all the factors of a number using its prime factorization?

Published on 25 Mar 2026 - 11:13

score 55 · Answer 5 · 2026-03-25 12:26:08

55

Views

Is $n! \nmid n^n$ true for every sufficiently large $n$ (maybe $n \ge 3$)?

Published on 25 Mar 2026 - 12:26

score 294 · Answer 6 · 2026-03-22 17:00:33

294

Views

Divisibility of a binomial coefficient by a prime

Published on 22 Mar 2026 - 17:00

score 94 · Answer 7 · 2026-03-25 13:57:58

94

Views

Can we find all solutions to the equation $\frac{\phi(n)}{\phi(n-1)}=5$, where $\phi(n)$ denotes the totient function?

Published on 25 Mar 2026 - 13:57

score 68 · Answer 8 · 2018-05-18 11:00:13

68

Views

Properties of modular arithmetic clarification

Published on 18 May 2018 - 11:00

score 244 · Answer 9 · 2026-03-25 07:46:23

Suppose for some positive integers r and s, the digits of $2^r$ is obtained by permuting the digits of $2^s$ in decimal expansion. Prove that $r = s$

score 150 · Answer 10 · 2018-05-19 23:20:28

150

Views

Find all $n$ for which $n^2+n+1$ is divisible by 73

Published on 19 May 2018 - 23:20

score 157 · Answer 11 · 2018-05-20 09:02:41

157

Views

find smallest integer $n$ greater than $1$ which satisfies the given condition .

Published on 20 May 2018 - 9:02

score 113 · Answer 12 · 2018-05-21 15:44:57

113

Views

Divisibility of an expression by 323

Published on 21 May 2018 - 15:44

score 312 · Answer 13 · 2018-05-21 16:12:41

312

Views

Find all integers $x$ and $y$ for which $\frac{x^2}{x-1}+\frac{y^2}{y-1}$ is an integer.

Published on 21 May 2018 - 16:12

score 115 · Answer 14 · 2026-03-25 12:25:34

115

Views

Is it correct: $1!+2!+\ldots+n!$ is not divisible by $n+1$ for $n\ge3$?

Published on 25 Mar 2026 - 12:25

score 57 · Answer 15 · 2026-03-25 09:43:06

57

Views

On the validity of a manual-calculation-friendly variation of the Legendre's formula: $\nu_p(n!)=\sum_{i=1}^\infty\lfloor\frac{n}{p^i}\rfloor$.

Published on 25 Mar 2026 - 9:43

List Question

Prove that $(n-2m)x^n-nx^{n-m}+nx^m-(n-2m)$ is divisble by $(x-1)^3$

How to find out if a polynomial has multiple roots?

Checking whether $4a2b$ is can be divided by $36$

How to get all the factors of a number using its prime factorization?

Is $n! \nmid n^n$ true for every sufficiently large $n$ (maybe $n \ge 3$)?

Divisibility of a binomial coefficient by a prime

Can we find all solutions to the equation $\frac{\phi(n)}{\phi(n-1)}=5$, where $\phi(n)$ denotes the totient function?

Properties of modular arithmetic clarification

Suppose for some positive integers r and s, the digits of $2^r$ is obtained by permuting the digits of $2^s$ in decimal expansion. Prove that $r = s$

Find all $n$ for which $n^2+n+1$ is divisible by 73

find smallest integer $n$ greater than $1$ which satisfies the given condition .

Divisibility of an expression by 323

Find all integers $x$ and $y$ for which $\frac{x^2}{x-1}+\frac{y^2}{y-1}$ is an integer.

Is it correct: $1!+2!+\ldots+n!$ is not divisible by $n+1$ for $n\ge3$?

On the validity of a manual-calculation-friendly variation of the Legendre's formula: $\nu_p(n!)=\sum_{i=1}^\infty\lfloor\frac{n}{p^i}\rfloor$.

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