Question

Show that there exists an integer $x$ such that $x\equiv 23 \mod 1000$ and $x\equiv 45 \mod 6789$

score 1.1k · Answer 1 · 2016-10-28 19:01:47

1.1k

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Show that there exists an integer $x$ such that $x\equiv 23 \mod 1000$ and $x\equiv 45 \mod 6789$

Published on 28 Oct 2016 - 19:01

score 106 · Answer 2 · 2016-10-29 06:20:48

106

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Find a permutation that satisfies this congruence

Published on 29 Oct 2016 - 6:20

score 134 · Answer 3 · 2016-10-30 00:40:18

134

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quadratic congruence using Newton-Raphson Method from calculus

Published on 30 Oct 2016 - 0:40

score 744 · Answer 4 · 2016-10-30 04:26:51

744

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Suppose that $p$ is a prime with $p \equiv 7 \pmod 8$. If $t = \frac{p - 1}{2}$ , prove that $2^t \equiv 1 \pmod p$

Published on 30 Oct 2016 - 4:26

score 304 · Answer 5 · 2016-10-30 18:41:43

304

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Can Fermat's Little Theorem be applied to non-integer rational numbers?

Published on 30 Oct 2016 - 18:41

score 489 · Answer 6 · 2016-10-31 16:17:26

489

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Remainder in polynomial division

Published on 31 Oct 2016 - 16:17

score 43 · Answer 7 · 2016-11-01 00:32:00

43

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solve congruence for m

Published on 01 Nov 2016 - 0:32

score 317 · Answer 8 · 2016-11-01 05:15:34

317

Views

Prove that if $r$ is a primitive root modulo $m$, and $(a, m) = (b, m) = 1$, then $r^a \equiv r^b \pmod{m}$ implies $a\equiv b \pmod{\varphi(m)}$

Published on 01 Nov 2016 - 5:15

score 394 · Answer 9 · 2016-11-01 13:33:27

394

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Let $p$ be an odd prime. Suppose that $a$ is an odd integer and also $a$ is a primitive root mod $p$. Show that $a$ is also a primitive root mod $2p$.

Published on 01 Nov 2016 - 13:33

score 120 · Answer 10 · 2026-03-25 14:26:58

120

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How to prove if $px+qy=r$ has an integer solution, then it has infinite integer solutions $(x,y)$ with $x$ being even or $y$ being even

Published on 25 Mar 2026 - 14:26

score 33 · Answer 11 · 2016-11-02 01:14:27

33

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Find all those $k$ for which $a_1 = a_2 = \cdots =a_n \pmod k$ where $k\ne1$

Published on 02 Nov 2016 - 1:14

score 869 · Answer 12 · 2016-11-02 03:04:05

869

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Prove that if ax+by=c has an integer solution, then it has infinitely many integer solutions (x, y) where x is even or y is even.

Published on 02 Nov 2016 - 3:04

score 421 · Answer 13 · 2016-11-02 06:49:19

421

Views

Proving that there is no integer solution to $3996x-3071y=-482$

Published on 02 Nov 2016 - 6:49

score 279 · Answer 14 · 2016-11-02 13:25:11

279

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Do there exist functions that grow faster than $ax+b$, slower than $a^x$ and still posses these nice congruence properties?

Published on 02 Nov 2016 - 13:25

score 129 · Answer 15 · 2016-11-03 15:18:18

129

Views

Congruence involving prime numbers

Published on 03 Nov 2016 - 15:18

List Question

Show that there exists an integer $x$ such that $x\equiv 23 \mod 1000$ and $x\equiv 45 \mod 6789$

Find a permutation that satisfies this congruence

quadratic congruence using Newton-Raphson Method from calculus

Suppose that $p$ is a prime with $p \equiv 7 \pmod 8$. If $t = \frac{p - 1}{2}$ , prove that $2^t \equiv 1 \pmod p$

Can Fermat's Little Theorem be applied to non-integer rational numbers?

Remainder in polynomial division

solve congruence for m

Prove that if $r$ is a primitive root modulo $m$, and $(a, m) = (b, m) = 1$, then $r^a \equiv r^b \pmod{m}$ implies $a\equiv b \pmod{\varphi(m)}$

Let $p$ be an odd prime. Suppose that $a$ is an odd integer and also $a$ is a primitive root mod $p$. Show that $a$ is also a primitive root mod $2p$.

How to prove if $px+qy=r$ has an integer solution, then it has infinite integer solutions $(x,y)$ with $x$ being even or $y$ being even

Find all those $k$ for which $a_1 = a_2 = \cdots =a_n \pmod k$ where $k\ne1$

Prove that if ax+by=c has an integer solution, then it has infinitely many integer solutions (x, y) where x is even or y is even.

Proving that there is no integer solution to $3996x-3071y=-482$

Do there exist functions that grow faster than $ax+b$, slower than $a^x$ and still posses these nice congruence properties?

Congruence involving prime numbers

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