Question

Is it true that $\underbrace{x^{x^{x^{.^{.^{.^x}}}}}}_{k\,\text{times}}\pmod9$ has period $18$ and can never take the values $3$ and $6$?

score 191 · Answer 1 · 2026-03-22 18:12:33

191

Views

Is it true that $\underbrace{x^{x^{x^{.^{.^{.^x}}}}}}_{k\,\text{times}}\pmod9$ has period $18$ and can never take the values $3$ and $6$?

Published on 22 Mar 2026 - 18:12

score 707 · Answer 2 · 2018-03-08 21:06:49

707

Views

Simplify $3^{2018}\pmod{31}$

Published on 08 Mar 2018 - 21:06

score 571 · Answer 3 · 2026-03-24 20:30:48

571

Views

Solving a cubic modular congruence

Published on 24 Mar 2026 - 20:30

score 39 · Answer 4 · 2026-03-25 12:45:38

39

Views

A simple modular arithmetic problem

Published on 25 Mar 2026 - 12:45

score 83 · Answer 5 · 2018-03-10 09:48:27

83

Views

How can I solve $2x+\sqrt {10} \equiv 10 \pmod{13}?$

Published on 10 Mar 2018 - 9:48

score 784 · Answer 6 · 2026-03-25 02:57:40

784

Views

Formula for Fibonacci sequence modulo 11

Published on 25 Mar 2026 - 2:57

score 26.6k · Answer 7 · 2018-03-11 08:33:03

26.6k

Views

Inverse of a modular matrix

Published on 11 Mar 2018 - 8:33

score 5k · Answer 8 · 2018-03-11 13:18:47

5k

Views

Modulus Operation with Negative Numbers

Published on 11 Mar 2018 - 13:18

score 122 · Answer 9 · 2026-03-25 06:22:13

122

Views

Let $e$ and $n$ be positive integers. Suppose $e$ and $φ(n)$ are relatively prime. Prove if $x^e ≡ 1\bmod(n)$, then $x ≡ 1\bmod(n)$

Published on 25 Mar 2026 - 6:22

score 19 · Answer 10 · 2026-03-25 04:43:44

19

Views

Is this an equivalent definition of the notation $f(x) \equiv g(x) \hspace{4mm} ( \text{mod} \hspace{2mm} h(x), \hspace{1mm} n )$?

Published on 25 Mar 2026 - 4:43

score 54 · Answer 11 · 2018-03-12 12:47:31

54

Views

Find r and n in congruence $827. 3^{839} ≡ r \mod n$

Published on 12 Mar 2018 - 12:47

score 343 · Answer 12 · 2026-03-23 07:21:10

343

Views

If $5x \equiv 15 \pmod{25}$, then definitely $x \equiv 3 \pmod{25}$. Is this true or false?

Published on 23 Mar 2026 - 7:21

score 282 · Answer 13 · 2018-03-12 13:35:53

282

Views

Solving the congruence $9x \equiv 3 \pmod{47}$

Published on 12 Mar 2018 - 13:35

score 50 · Answer 14 · 2018-03-12 18:01:45

50

Views

Proving $x ≡ y \pmod n $ if $x^a ≡ y^a \pmod n$

Published on 12 Mar 2018 - 18:01

score 146 · Answer 15 · 2018-03-12 19:08:24

146

Views

Properties of the "eeny, meeny, miny, moe function"

Published on 12 Mar 2018 - 19:08

List Question

Is it true that $\underbrace{x^{x^{x^{.^{.^{.^x}}}}}}_{k\,\text{times}}\pmod9$ has period $18$ and can never take the values $3$ and $6$?

Simplify $3^{2018}\pmod{31}$

Solving a cubic modular congruence

A simple modular arithmetic problem

How can I solve $2x+\sqrt {10} \equiv 10 \pmod{13}?$

Formula for Fibonacci sequence modulo 11

Inverse of a modular matrix

Modulus Operation with Negative Numbers

Let $e$ and $n$ be positive integers. Suppose $e$ and $φ(n)$ are relatively prime. Prove if $x^e ≡ 1\bmod(n)$, then $x ≡ 1\bmod(n)$

Is this an equivalent definition of the notation $f(x) \equiv g(x) \hspace{4mm} ( \text{mod} \hspace{2mm} h(x), \hspace{1mm} n )$?

Find r and n in congruence $827. 3^{839} ≡ r \mod n$

If $5x \equiv 15 \pmod{25}$, then definitely $x \equiv 3 \pmod{25}$. Is this true or false?

Solving the congruence $9x \equiv 3 \pmod{47}$

Proving $x ≡ y \pmod n $ if $x^a ≡ y^a \pmod n$

Properties of the "eeny, meeny, miny, moe function"

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