Question

Find all positive integer $m$ such that $3^m+81$ is a perfect square.

score 75 · Answer 1 · 2023-05-08 00:48:38

75

Views

Find all positive integer $m$ such that $3^m+81$ is a perfect square.

Published on 08 May 2023 - 0:48

score 204 · Answer 2 · 2023-05-08 17:57:13

204

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The number of positive integers n less than or equal to $22$ such that $7$ divides $n^5 +4n^4 +3n^3 +2022$

Published on 08 May 2023 - 17:57

score 22 · Answer 3 · 2023-05-11 16:44:44

If $a_1, a_2, \cdots, a_n$ are two-to-two relative prime integers (n ≥ 2) and for each i, i =1, 2, . ., n, $a_i|c$, prove that $a_1*a_2 · · · a_n|c$

score 55 · Answer 4 · 2023-05-15 03:23:04

55

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Find all the values of a,b,c s.t that x divides $a^2-cb,c^2-ab,b^2-ac$ where x is an integer

Published on 15 May 2023 - 3:23

score 276 · Answer 5 · 2023-05-15 04:39:39

276

Views

Find all integers $n$ such that $(n - 1)^2 + 3$ divides $n^3 + 2023$.

Published on 15 May 2023 - 4:39

score 108 · Answer 6 · 2026-03-25 16:46:29

108

Views

On a conjecture involving multiplicative functions and the integers $1836$ and $136$

Published on 25 Mar 2026 - 16:46

score 60 · Answer 7 · 2026-03-25 14:36:41

60

Views

Number of divisors of composite number between and adjacent to twin primes

Published on 25 Mar 2026 - 14:36

score 139 · Answer 8 · 2026-03-25 16:46:30

139

Views

On a conjecture involving multiplicative functions and the integers $1836$ and $137$

Published on 25 Mar 2026 - 16:46

score 110 · Answer 9 · 2026-04-04 00:10:30

110

Views

Checking when quotient of polynomials is integer

Published on 04 Apr 2026 - 0:10

score 195 · Answer 10 · 2026-03-26 01:34:36

195

Views

Are there infinitely many $c$-th perfect powers having a constant congruence speed of $c$?

Published on 26 Mar 2026 - 1:34

score 96 · Answer 11 · 2026-02-24 17:18:53

96

Views

In a division, why is every common divisor of the divisor and the remainder also a divisor of the dividend?

Published on 24 Feb 2026 - 17:18

score 140 · Answer 12 · 2026-04-02 06:31:11

140

Views

What is the fastest way to write an even number as the sum of two primes?

Published on 02 Apr 2026 - 6:31

score 160 · Answer 13 · 2026-03-26 16:06:44

160

Views

Proving the Existence of a Number without Constructing

Published on 26 Mar 2026 - 16:06

score 512 · Answer 14 · 2023-06-05 20:45:52

512

Views

find infinitely many (or all) positive integers n so that n and rev(n) are perfect squares

Published on 05 Jun 2023 - 20:45

score 41 · Answer 15 · 2026-02-23 13:43:09

41

Views

Possible values of $\gcd(2a^2+6a-4, 2a^2+4a-3)$

Published on 23 Feb 2026 - 13:43

List Question

Find all positive integer $m$ such that $3^m+81$ is a perfect square.

The number of positive integers n less than or equal to $22$ such that $7$ divides $n^5 +4n^4 +3n^3 +2022$

If $a_1, a_2, \cdots, a_n$ are two-to-two relative prime integers (n ≥ 2) and for each i, i =1, 2, . ., n, $a_i|c$, prove that $a_1*a_2 · · · a_n|c$

Find all the values of a,b,c s.t that x divides $a^2-cb,c^2-ab,b^2-ac$ where x is an integer

Find all integers $n$ such that $(n - 1)^2 + 3$ divides $n^3 + 2023$.

On a conjecture involving multiplicative functions and the integers $1836$ and $136$

Number of divisors of composite number between and adjacent to twin primes

On a conjecture involving multiplicative functions and the integers $1836$ and $137$

Checking when quotient of polynomials is integer

Are there infinitely many $c$-th perfect powers having a constant congruence speed of $c$?

In a division, why is every common divisor of the divisor and the remainder also a divisor of the dividend?

What is the fastest way to write an even number as the sum of two primes?

Proving the Existence of a Number without Constructing

find infinitely many (or all) positive integers n so that n and rev(n) are perfect squares

Possible values of $\gcd(2a^2+6a-4, 2a^2+4a-3)$

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