Question

How to rewrite a decimal number $x$ as $1.y\cdot2^{n}$?

score 37 · Answer 1 · 2026-04-13 21:10:02

37

Views

How to rewrite a decimal number $x$ as $1.y\cdot2^{n}$?

Published on 13 Apr 2026 - 21:10

score 1.1k · Answer 2 · 2026-04-16 14:26:43

1.1k

Views

Prove $n=m^3-3m^2+2m$, for any integer $m$, then $n$ is a multiple of $6$.

Published on 16 Apr 2026 - 14:26

score 196 · Answer 3 · 2026-04-13 18:04:01

196

Views

Does the order of $2$ in $Z_p$ divide the order of $2$ in $Z_n$?

Published on 13 Apr 2026 - 18:04

score 146 · Answer 4 · 2026-04-17 11:55:44

146

Views

Prove that every prime number divides some number in the sequence $ a_n = 2^n+3^n+6^n-1 $

Published on 17 Apr 2026 - 11:55

score 2.1k · Answer 5 · 2026-04-15 21:25:31

2.1k

Views

Let k be an integer. Disprove: “The equation $x^2 − x − k = 0$ has no integer solution if and only if $k$ is odd.”

Published on 15 Apr 2026 - 21:25

score 170 · Answer 6 · 2026-04-19 08:06:49

170

Views

Is the function $f(n)=\varphi(n)+\varphi(n+1)-n$ surjective?

Published on 19 Apr 2026 - 8:06

score 3.1k · Answer 7 · 2026-04-16 14:35:09

3.1k

Views

Prove that $n! > n^{3}$ for every integer $n \ge 6$ using induction

Published on 16 Apr 2026 - 14:35

score 116 · Answer 8 · 2026-04-10 03:24:17

116

Views

Writing of congruences with negatives

Published on 10 Apr 2026 - 3:24

score 222 · Answer 9 · 2026-04-09 05:53:31

222

Views

Stapled sequences- set of consecutive positive integers such that no one of them is relatively prime with all of the others

Published on 09 Apr 2026 - 5:53

score 107 · Answer 10 · 2026-04-16 17:28:29

107

Views

solution of an algebraic equation with integers

Published on 16 Apr 2026 - 17:28

score 70 · Answer 11 · 2026-04-16 08:27:35

70

Views

Find all $n$ such that the following is prime

Published on 16 Apr 2026 - 8:27

score 132 · Answer 12 · 2026-04-10 13:59:44

132

Views

Dividing every term in congruence

Published on 10 Apr 2026 - 13:59

score 166 · Answer 13 · 2026-04-15 02:57:28

166

Views

Distinct integer solutions to the equation $(x^2+y^2+z^2)/(x+y+z)=2n$

Published on 15 Apr 2026 - 2:57

score 450 · Answer 14 · 2026-05-11 07:24:33

450

Views

What is the value of $abc0ac$, a six digit perfect square number which is divisible by $5$ and $11$?

Published on 11 May 2026 - 7:24

score 122 · Answer 15 · 2026-04-09 04:18:45

122

Views

Is it possible to find a closed form using modular arithmetic?

Published on 09 Apr 2026 - 4:18

List Question

How to rewrite a decimal number $x$ as $1.y\cdot2^{n}$?

Prove $n=m^3-3m^2+2m$, for any integer $m$, then $n$ is a multiple of $6$.

Does the order of $2$ in $Z_p$ divide the order of $2$ in $Z_n$?

Prove that every prime number divides some number in the sequence $ a_n = 2^n+3^n+6^n-1 $

Let k be an integer. Disprove: “The equation $x^2 − x − k = 0$ has no integer solution if and only if $k$ is odd.”

Is the function $f(n)=\varphi(n)+\varphi(n+1)-n$ surjective?

Prove that $n! > n^{3}$ for every integer $n \ge 6$ using induction

Writing of congruences with negatives

Stapled sequences- set of consecutive positive integers such that no one of them is relatively prime with all of the others

solution of an algebraic equation with integers

Find all $n$ such that the following is prime

Dividing every term in congruence

Distinct integer solutions to the equation $(x^2+y^2+z^2)/(x+y+z)=2n$

What is the value of $abc0ac$, a six digit perfect square number which is divisible by $5$ and $11$?

Is it possible to find a closed form using modular arithmetic?

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