List questions from congruences

Published on 20 Apr 2015 - 3:42

679

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If $n\equiv 4 \pmod 9$ then $n$ cannot be written as sum of three cubes?

Published on 22 Apr 2015 - 3:25

59

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Show that if $x\equiv 1 \pmod {m^k}, $then $x^m \equiv 1\pmod{m^{k+1}}$.

Published on 22 Apr 2015 - 4:19

1.2k

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I finally understand simple congruences. Now how to solve a quadratic congruence?

Published on 23 Apr 2015 - 0:51

253

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Basic question about modular arithmetic applied to the divisor sum function $\sigma(n)$ when $n=5p$

Published on 24 Apr 2015 - 4:12

338

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What is the ten's digit of $7^{7^{7^{7^7}}}$

Published on 25 Apr 2015 - 11:37

60

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Number Theory Simple Proof

Published on 27 Apr 2015 - 22:13

59

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If $2^{12^{7}+3}\equiv x \pmod{36}$, then what is the value of $x$?

Published on 28 Apr 2015 - 15:02

85

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Trouble forming general solution for linear congruence

Published on 29 Apr 2015 - 15:02

208

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Is $p \equiv q\pmod{15}$ the same as $p\equiv q\pmod{5}$?

Published on 30 Apr 2015 - 6:04

105

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$5x\equiv3\pmod3$

Published on 01 May 2015 - 4:39

851

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Show that for any prime $ p $, there are integers $ x $ and $ y $ such that $ p|(x^{2} + y^{2} + 1) $.

Published on 28 Mar 2026 - 6:00

805

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How many solutions to $x^d\equiv a\pmod {p}$?

Published on 02 May 2015 - 11:27

3.6k

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Needing help finding the least nonnegative residue

Published on 03 May 2015 - 0:58

410

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If $ p $ is an odd prime and $ D $ an integer not divisible by $ p $, show that $ x^2 - y^2 \equiv D ~ (\text{mod} ~ p) $ has $ (p - 1) $ solutions.

Published on 28 Mar 2026 - 5:59

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The order of an element

If $n\equiv 4 \pmod 9$ then $n$ cannot be written as sum of three cubes?

Show that if $x\equiv 1 \pmod {m^k}, $then $x^m \equiv 1\pmod{m^{k+1}}$.

I finally understand simple congruences. Now how to solve a quadratic congruence?

Basic question about modular arithmetic applied to the divisor sum function $\sigma(n)$ when $n=5p$

What is the ten's digit of $7^{7^{7^{7^7}}}$

Number Theory Simple Proof

If $2^{12^{7}+3}\equiv x \pmod{36}$, then what is the value of $x$?

Trouble forming general solution for linear congruence

Is $p \equiv q\pmod{15}$ the same as $p\equiv q\pmod{5}$?

$5x\equiv3\pmod3$

Show that for any prime $ p $, there are integers $ x $ and $ y $ such that $ p|(x^{2} + y^{2} + 1) $.

How many solutions to $x^d\equiv a\pmod {p}$?

Needing help finding the least nonnegative residue

If $ p $ is an odd prime and $ D $ an integer not divisible by $ p $, show that $ x^2 - y^2 \equiv D ~ (\text{mod} ~ p) $ has $ (p - 1) $ solutions.

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