Question

Two disjoint sets $A$ and $B$ such that the product of numbers in $A$ is congruent to product of numbers in $B$ modulo $n$.

score 42 · Answer 1 · 2023-04-11 23:30:07

42

Views

Two disjoint sets $A$ and $B$ such that the product of numbers in $A$ is congruent to product of numbers in $B$ modulo $n$.

Published on 11 Apr 2023 - 23:30

score 86 · Answer 2 · 2023-04-12 00:16:31

86

Views

Determine all positive integers $n^6-1$ divisible by each of $2,3,5,7,13$.

Published on 12 Apr 2023 - 0:16

score 31 · Answer 3 · 2023-04-12 19:16:28

31

Views

How to prove that $\overline{a_na_{n-1}...a_ka_{k-1}...a_0} ≡ \overline{a_{k-1}a_{k-2}...a_0}$ mod($5^k$)?

Published on 12 Apr 2023 - 19:16

score 98 · Answer 4 · 2026-03-30 06:22:05

98

Views

Multiplicative lattice with $(a \land b)\ast(a\lor b)=a \ast b$

Published on 30 Mar 2026 - 6:22

score 320 · Answer 5 · 2023-04-17 02:45:17

320

Views

How many 5 digit positive integers are divisible by 5 and without repetition of digits?

Published on 17 Apr 2023 - 2:45

score 89 · Answer 6 · 2026-03-20 19:02:26

89

Views

Prove that the degree of every irreducible representation divides $[ G : Z(G) ]$

Published on 20 Mar 2026 - 19:02

score 93 · Answer 7 · 2026-04-03 08:04:51

93

Views

Prove the divisibility of the polynomial $x f'(x) - n f(x)$

Published on 03 Apr 2026 - 8:04

score 53 · Answer 8 · 2023-04-20 17:36:10

53

Views

Searching for a reference on a congruence relation

Published on 20 Apr 2023 - 17:36

score 57 · Answer 9 · 2023-04-23 19:26:28

57

Views

Divisibility of a number in base-10?

Published on 23 Apr 2023 - 19:26

score 52 · Answer 10 · 2023-04-25 02:30:04

52

Views

If $x$ divides both $y_1z_1$ and $y_2z_2$ then $x$ divides both $z_1, z_2$.

Published on 25 Apr 2023 - 2:30

score 190 · Answer 11 · 2023-04-26 03:29:44

190

Views

If $(\gcd(a,b), \gcd(b,c), \gcd(c,a))$ form a triangle, what is the probability that $(a,b,c)$ also form a triangle?

Published on 26 Apr 2023 - 3:29

score 55 · Answer 12 · 2023-05-05 06:48:26

55

Views

Show that if $n \mid (p-1)$ and $p \mid (n^4+n^3-n-1)$, then $4p-3$ is a quadratic number.

Published on 05 May 2023 - 6:48

score 197 · Answer 13 · 2023-05-06 05:44:48

197

Views

Find all relative prime positive integers $p$ and $q$ such that $p+q=(p-q)^3$.

Published on 06 May 2023 - 5:44

score 81 · Answer 14 · 2023-05-07 15:57:28

81

Views

What number is n if n-1 is divisible by 15 and n+1 divides 1001?

Published on 07 May 2023 - 15:57

score 218 · Answer 15 · 2023-05-07 16:08:29

218

Views

Show that infinitely many odd $n$ divide $2023^n-1$

Published on 07 May 2023 - 16:08

List Question

Two disjoint sets $A$ and $B$ such that the product of numbers in $A$ is congruent to product of numbers in $B$ modulo $n$.

Determine all positive integers $n^6-1$ divisible by each of $2,3,5,7,13$.

How to prove that $\overline{a_na_{n-1}...a_ka_{k-1}...a_0} ≡ \overline{a_{k-1}a_{k-2}...a_0}$ mod($5^k$)?

Multiplicative lattice with $(a \land b)\ast(a\lor b)=a \ast b$

How many 5 digit positive integers are divisible by 5 and without repetition of digits?

Prove that the degree of every irreducible representation divides $[ G : Z(G) ]$

Prove the divisibility of the polynomial $x f'(x) - n f(x)$

Searching for a reference on a congruence relation

Divisibility of a number in base-10?

If $x$ divides both $y_1z_1$ and $y_2z_2$ then $x$ divides both $z_1, z_2$.

If $(\gcd(a,b), \gcd(b,c), \gcd(c,a))$ form a triangle, what is the probability that $(a,b,c)$ also form a triangle?

Show that if $n \mid (p-1)$ and $p \mid (n^4+n^3-n-1)$, then $4p-3$ is a quadratic number.

Find all relative prime positive integers $p$ and $q$ such that $p+q=(p-q)^3$.

What number is n if n-1 is divisible by 15 and n+1 divides 1001?

Show that infinitely many odd $n$ divide $2023^n-1$

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