Question

Solving Systems of Congruence using CRT

score 41 · Answer 1 · 2016-10-16 10:28:03

41

Views

Solving Systems of Congruence using CRT

Published on 16 Oct 2016 - 10:28

score 143 · Answer 2 · 2016-10-16 21:53:14

143

Views

Show that if p is prime and $p \nshortmid abc$ then the congruence $ax^2 + by^2 + cz^2 \equiv 0 \pmod p$ has a solution other than $(0,0,0)$

Published on 16 Oct 2016 - 21:53

score 950 · Answer 3 · 2016-10-18 01:34:23

950

Views

If a is congruent to b(mod m) and c is congruent to d(mod m) then a^c is congruent to b^d(mod m)

Published on 18 Oct 2016 - 1:34

score 57 · Answer 4 · 2016-10-18 04:07:39

57

Views

Justification for solving modular congruencies

Published on 18 Oct 2016 - 4:07

score 1.4k · Answer 5 · 2016-10-19 02:51:43

1.4k

Views

Prove no solution to $x^2\equiv3\bmod5$

Published on 19 Oct 2016 - 2:51

score 1.1k · Answer 6 · 2026-03-22 12:27:09

1.1k

Views

solve x for a cubic congruence equation with large prime mod.

Published on 22 Mar 2026 - 12:27

score 497 · Answer 7 · 2016-10-20 08:50:31

497

Views

If $p$ is an odd prime and $\gcd(ab, p) = 1$, prove that at least one of $a, b$, or $ab$ is a quadratic residue of p.

Published on 20 Oct 2016 - 8:50

score 447 · Answer 8 · 2016-10-20 15:51:55

447

Views

sum of digits for a number thats a multiple of 9 , induction

Published on 20 Oct 2016 - 15:51

score 221 · Answer 9 · 2016-10-21 10:48:34

221

Views

Modulus proof with factorials

Published on 21 Oct 2016 - 10:48

score 1k · Answer 10 · 2016-10-21 12:17:49

1k

Views

Solve $x^2 + x + 47 ≡ 0 \pmod {7^3}$

Published on 21 Oct 2016 - 12:17

score 162 · Answer 11 · 2016-10-23 00:00:22

162

Views

How to prove $(11k + 5, 8 + 15k) > 1 \implies (11k + 5, 8 + 15k) = 13 \implies k \equiv 9 \pmod {13}$?

Published on 23 Oct 2016 - 0:00

score 63 · Answer 12 · 2016-10-23 17:08:46

63

Views

Given $x^{93} \equiv 2 \, (\textrm{mod}\ 5)$, $x \equiv \,? \, (\textrm{mod}\ 5)$

Published on 23 Oct 2016 - 17:08

score 59 · Answer 13 · 2026-03-26 14:22:54

59

Views

Show $(a,b)$ is in the equivalence relation $L_s$ iff $(ap,bp)$ is in $L_{s/p}$ where p is a congruence on semigroup S

Published on 26 Mar 2026 - 14:22

score 695 · Answer 14 · 2016-10-26 15:43:13

695

Views

System of linear congruences modulo a prime power

Published on 26 Oct 2016 - 15:43

score 65 · Answer 15 · 2016-10-28 09:27:26

65

Views

Why $A(d) = {\{x \ : \ 1 \le x \le p - 1 \ \ \text{and}\ \ \text{exp}_p(x) = d}\}$ are disjoint?

Published on 28 Oct 2016 - 9:27

List Question

Solving Systems of Congruence using CRT

Show that if p is prime and $p \nshortmid abc$ then the congruence $ax^2 + by^2 + cz^2 \equiv 0 \pmod p$ has a solution other than $(0,0,0)$

If a is congruent to b(mod m) and c is congruent to d(mod m) then a^c is congruent to b^d(mod m)

Justification for solving modular congruencies

Prove no solution to $x^2\equiv3\bmod5$

solve x for a cubic congruence equation with large prime mod.

If $p$ is an odd prime and $\gcd(ab, p) = 1$, prove that at least one of $a, b$, or $ab$ is a quadratic residue of p.

sum of digits for a number thats a multiple of 9 , induction

Modulus proof with factorials

Solve $x^2 + x + 47 ≡ 0 \pmod {7^3}$

How to prove $(11k + 5, 8 + 15k) > 1 \implies (11k + 5, 8 + 15k) = 13 \implies k \equiv 9 \pmod {13}$?

Given $x^{93} \equiv 2 \, (\textrm{mod}\ 5)$, $x \equiv \,? \, (\textrm{mod}\ 5)$

Show $(a,b)$ is in the equivalence relation $L_s$ iff $(ap,bp)$ is in $L_{s/p}$ where p is a congruence on semigroup S

System of linear congruences modulo a prime power

Why $A(d) = {\{x \ : \ 1 \le x \le p - 1 \ \ \text{and}\ \ \text{exp}_p(x) = d}\}$ are disjoint?

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