Question

If $a,m,n \in \mathbb{Z}$ with $m>0, n >0$, Prove that [$a^m]=[a^n]$ in $\mathbb{Z_2},$

score 43 · Answer 1 · 2013-09-24 02:59:25

43

Views

If $a,m,n \in \mathbb{Z}$ with $m>0, n >0$, Prove that [$a^m]=[a^n]$ in $\mathbb{Z_2},$

Published on 24 Sep 2013 - 2:59

score 655 · Answer 2 · 2026-03-30 04:00:18

655

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Question about corollary of Euler's theorem

Published on 30 Mar 2026 - 4:00

score 325 · Answer 3 · 2013-09-28 18:32:43

325

Views

Solution to linear congruences

Published on 28 Sep 2013 - 18:32

score 76 · Answer 4 · 2013-10-01 12:41:11

76

Views

If $a+b\equiv0\pmod m$ and $c+d\equiv 0\pmod m$ then $ac\equiv bd\pmod m$. Demonstration.

Published on 01 Oct 2013 - 12:41

score 41 · Answer 5 · 2013-10-01 13:27:25

41

Views

If $a\equiv b\pmod m$ and $c+d\equiv 0\pmod m$ then $ac+bd\equiv 0\pmod m$

Published on 01 Oct 2013 - 13:27

score 87 · Answer 6 · 2013-10-01 13:51:42

87

Views

If $a,p\in\mathbb{N}$ with $p$ prime, have to show that if $a²\equiv1\pmod p $, then $a\equiv1\pmod p$ or $a\equiv p-1\pmod p$

Published on 01 Oct 2013 - 13:51

score 234 · Answer 7 · 2013-10-01 17:40:09

234

Views

What is the remainder of dividing $14^{256}$ by $17$?

Published on 01 Oct 2013 - 17:40

score 154 · Answer 8 · 2013-10-01 17:50:38

154

Views

What is the remainder of dividing $(116+17^{17})^{21}$ by $8$?

Published on 01 Oct 2013 - 17:50

score 144 · Answer 9 · 2013-10-01 19:20:31

144

Views

Prove that every odd prime divisor of $n^2+100$ is of the form $12k+1$ or $12k+5$

Published on 01 Oct 2013 - 19:20

score 152 · Answer 10 · 2013-10-02 07:29:23

152

Views

Show that there exist infinitely many primes of the form $6k-1$

Published on 02 Oct 2013 - 7:29

score 267 · Answer 11 · 2013-10-02 22:25:31

267

Views

Show that $x^2+5y^2=2z^2$ has only trivial solution $(x,y,z)=(0,0,0)$

Published on 02 Oct 2013 - 22:25

score 604 · Answer 12 · 2013-10-04 04:10:28

604

Views

Proving divisibility without an inductive proof.

Published on 04 Oct 2013 - 4:10

score 66 · Answer 13 · 2013-10-06 02:02:30

66

Views

Demonstration congruences

Published on 06 Oct 2013 - 2:02

score 464 · Answer 14 · 2013-10-06 03:31:39

464

Views

centenes of $7^{999999}$

Published on 06 Oct 2013 - 3:31

score 127 · Answer 15 · 2013-10-06 14:35:11

127

Views

Polynomial Congruences

Published on 06 Oct 2013 - 14:35

List Question

If $a,m,n \in \mathbb{Z}$ with $m>0, n >0$, Prove that [$a^m]=[a^n]$ in $\mathbb{Z_2},$

Question about corollary of Euler's theorem

Solution to linear congruences

If $a+b\equiv0\pmod m$ and $c+d\equiv 0\pmod m$ then $ac\equiv bd\pmod m$. Demonstration.

If $a\equiv b\pmod m$ and $c+d\equiv 0\pmod m$ then $ac+bd\equiv 0\pmod m$

If $a,p\in\mathbb{N}$ with $p$ prime, have to show that if $a²\equiv1\pmod p $, then $a\equiv1\pmod p$ or $a\equiv p-1\pmod p$

What is the remainder of dividing $14^{256}$ by $17$?

What is the remainder of dividing $(116+17^{17})^{21}$ by $8$?

Prove that every odd prime divisor of $n^2+100$ is of the form $12k+1$ or $12k+5$

Show that there exist infinitely many primes of the form $6k-1$

Show that $x^2+5y^2=2z^2$ has only trivial solution $(x,y,z)=(0,0,0)$

Proving divisibility without an inductive proof.

Demonstration congruences

centenes of $7^{999999}$

Polynomial Congruences

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