Question

Prove $1+a^{p-1}+...a^{(p-1)^2}$ is divisible by prime p,given a and p are co-prime.

score 49 · Answer 1 · 2026-03-22 19:28:40

49

Views

Prove $1+a^{p-1}+...a^{(p-1)^2}$ is divisible by prime p,given a and p are co-prime.

Published on 22 Mar 2026 - 19:28

score 1.2k · Answer 2 · 2026-04-07 14:19:45

1.2k

Views

Prove that a number composed of only $2n$ "1"s, minus another number composed of only $n$ "2"s, is a perfect square.

Published on 07 Apr 2026 - 14:19

score 783 · Answer 3 · 2026-03-25 03:19:41

783

Views

How to find remainder when $2^{2018}$ is divided by 43?

Published on 25 Mar 2026 - 3:19

score 605 · Answer 4 · 2026-03-25 03:20:20

605

Views

If $a^2 \equiv 4 \pmod{5}$, then $a \equiv 2 \pmod{5}$.

Published on 25 Mar 2026 - 3:20

score 325 · Answer 5 · 2026-03-25 06:13:05

325

Views

Suppose that for all integers $x$, $x|a$ and $x|b$ if and only if $x|c$. Then $c = \gcd(a,b)$

Published on 25 Mar 2026 - 6:13

score 71 · Answer 6 · 2026-04-09 02:41:25

71

Views

Showing two different definitions of a primitive root are the same

Published on 09 Apr 2026 - 2:41

score 87 · Answer 7 · 2026-03-23 04:55:55

87

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Solve $\gcd(a,b)=2$, $3a+b^2 =3388$, $a>0$, $b>49$

Published on 23 Mar 2026 - 4:55

score 231 · Answer 8 · 2026-03-25 03:04:02

231

Views

Periodicity of $a_n={n \choose z}\ mod \ y$?

Published on 25 Mar 2026 - 3:04

score 230 · Answer 9 · 2026-04-09 02:55:14

230

Views

If $x^2-dy^2 = -1$ has a solution in $\mathbb{Z^2}$, then $d$ is the sum of two coprime squares.

Published on 09 Apr 2026 - 2:55

score 239 · Answer 10 · 2026-03-25 19:05:05

239

Views

Use the definition to prove for all natural number m, 4m+ 7 odd.

Published on 25 Mar 2026 - 19:05

score 119 · Answer 11 · 2026-03-25 01:18:46

119

Views

Prime factors of $5 n^4 - 70 n^3 + 380 n^2 - 945 n + 911 $

Published on 25 Mar 2026 - 1:18

score 60 · Answer 12 · 2026-03-25 07:45:46

60

Views

S is the set of all numbers of the form $4n+1$ where $n \geq 1$

Published on 25 Mar 2026 - 7:45

score 103 · Answer 13 · 2026-03-25 06:06:54

103

Views

Prove that the set of all prime numbers of the form $6n+5$ is infinite

Published on 25 Mar 2026 - 6:06

score 235 · Answer 14 · 2026-03-24 22:07:48

235

Views

Find all the digits $a,b$ in such a way that $n=62ab427$ is multiple of $99$

Published on 24 Mar 2026 - 22:07

score 127 · Answer 15 · 2026-04-05 16:49:01

127

Views

A problem of Number Theory

Published on 05 Apr 2026 - 16:49

List Question

Prove $1+a^{p-1}+...a^{(p-1)^2}$ is divisible by prime p,given a and p are co-prime.

Prove that a number composed of only $2n$ "1"s, minus another number composed of only $n$ "2"s, is a perfect square.

How to find remainder when $2^{2018}$ is divided by 43?

If $a^2 \equiv 4 \pmod{5}$, then $a \equiv 2 \pmod{5}$.

Suppose that for all integers $x$, $x|a$ and $x|b$ if and only if $x|c$. Then $c = \gcd(a,b)$

Showing two different definitions of a primitive root are the same

Solve $\gcd(a,b)=2$, $3a+b^2 =3388$, $a>0$, $b>49$

Periodicity of $a_n={n \choose z}\ mod \ y$?

If $x^2-dy^2 = -1$ has a solution in $\mathbb{Z^2}$, then $d$ is the sum of two coprime squares.

Use the definition to prove for all natural number m, 4m+ 7 odd.

Prime factors of $5 n^4 - 70 n^3 + 380 n^2 - 945 n + 911 $

S is the set of all numbers of the form $4n+1$ where $n \geq 1$

Prove that the set of all prime numbers of the form $6n+5$ is infinite

Find all the digits $a,b$ in such a way that $n=62ab427$ is multiple of $99$

A problem of Number Theory

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