Question

Find $a+b$ for $a, b$ such that $(x+1)^{n}(x^{2}+ax+b) \equiv 2^{n}(x-1) \mod (x-1)^{2}$

score 34 · Answer 1 · 2015-02-09 06:13:13

34

Views

Find $a+b$ for $a, b$ such that $(x+1)^{n}(x^{2}+ax+b) \equiv 2^{n}(x-1) \mod (x-1)^{2}$

Published on 09 Feb 2015 - 6:13

score 25 · Answer 2 · 2015-02-09 12:53:17

25

Views

If $n \in \mathbb Z^+$ , $a,b$ are integers such that $d=g.c.d.(a-b,n)$ , then $d^2|a^n-b^n$ ?

Published on 09 Feb 2015 - 12:53

score 479 · Answer 3 · 2026-03-25 17:18:49

479

Views

Solve: $ab+bc+ca\mid (a+b+c)^2$

Published on 25 Mar 2026 - 17:18

score 21.7k · Answer 4 · 2026-04-09 02:36:21

21.7k

Views

Formula of MIPS (million instructions per second)

Published on 09 Apr 2026 - 2:36

score 130 · Answer 5 · 2015-02-10 03:43:58

130

Views

Prove that if $na=mb$ and $(a,b)=1$, then $m=a$ and $n=b$.

Published on 10 Feb 2015 - 3:43

score 86 · Answer 6 · 2015-02-10 15:11:04

86

Views

To prove for every integer $k >1 $ , $2+2^k \choose r$ is even for all $2 < r \le n=1+2^{k-1}$ , without Lucas' theorem

Published on 10 Feb 2015 - 15:11

score 256 · Answer 7 · 2015-02-10 16:05:07

256

Views

Proof verification ($p$ prime then $p\mid \binom{p}{k}$ for $1\le k\le p-1$)

Published on 10 Feb 2015 - 16:05

score 333 · Answer 8 · 2026-04-07 19:32:49

333

Views

How does author reach step of $sa + tm \equiv 1 \pmod m$?

Published on 07 Apr 2026 - 19:32

score 122 · Answer 9 · 2015-02-11 13:13:34

122

Views

Use of GCD Distributive Law in proof of Euclid's Lemma

Published on 11 Feb 2015 - 13:13

score 708 · Answer 10 · 2015-02-11 13:30:29

708

Views

$n,a,b \mathbb \in \mathbb Z^+$ , such that $n\mid a^n-b^n$ ; to show $n\mid \frac {a^n-b^n}{a-b}$

Published on 11 Feb 2015 - 13:30

score 988 · Answer 11 · 2015-02-11 14:10:06

988

Views

Let $a,b$ be positive integers such that $a\mid b^2 , b^2\mid a^3 , a^3\mid b^4 \ldots$ so on , then $a=b$?

Published on 11 Feb 2015 - 14:10

score 59 · Answer 12 · 2015-02-11 16:30:31

59

Views

Form of Divisors of Proth numbers

Published on 11 Feb 2015 - 16:30

score 53 · Answer 13 · 2015-02-11 17:47:17

53

Views

Number theory hcf confusion

Published on 11 Feb 2015 - 17:47

score 309 · Answer 14 · 2015-02-12 03:40:14

309

Views

Prove that $(z^3-z)(z+2)$ is divisible by $12$ for all integers $z$

Published on 12 Feb 2015 - 3:40

score 47 · Answer 15 · 2015-02-12 13:09:21

47

Views

Does $ p|(2^{2kq}-2^{kq}+1)$ where $p=1+k\cdot q$ ? I'm stuck...

Published on 12 Feb 2015 - 13:09

List Question

Find $a+b$ for $a, b$ such that $(x+1)^{n}(x^{2}+ax+b) \equiv 2^{n}(x-1) \mod (x-1)^{2}$

If $n \in \mathbb Z^+$ , $a,b$ are integers such that $d=g.c.d.(a-b,n)$ , then $d^2|a^n-b^n$ ?

Solve: $ab+bc+ca\mid (a+b+c)^2$

Formula of MIPS (million instructions per second)

Prove that if $na=mb$ and $(a,b)=1$, then $m=a$ and $n=b$.

To prove for every integer $k >1 $ , $2+2^k \choose r$ is even for all $2 < r \le n=1+2^{k-1}$ , without Lucas' theorem

Proof verification ($p$ prime then $p\mid \binom{p}{k}$ for $1\le k\le p-1$)

How does author reach step of $sa + tm \equiv 1 \pmod m$?

Use of GCD Distributive Law in proof of Euclid's Lemma

$n,a,b \mathbb \in \mathbb Z^+$ , such that $n\mid a^n-b^n$ ; to show $n\mid \frac {a^n-b^n}{a-b}$

Let $a,b$ be positive integers such that $a\mid b^2 , b^2\mid a^3 , a^3\mid b^4 \ldots$ so on , then $a=b$?

Form of Divisors of Proth numbers

Number theory hcf confusion

Prove that $(z^3-z)(z+2)$ is divisible by $12$ for all integers $z$

Does $ p|(2^{2kq}-2^{kq}+1)$ where $p=1+k\cdot q$ ? I'm stuck...

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