Question

order n polynomial long division question

score 64 · Answer 1 · 2023-03-07 05:32:11

64

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order n polynomial long division question

Published on 07 Mar 2023 - 5:32

score 117 · Answer 2 · 2026-04-07 09:46:02

117

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What is the limiting mean value of the product of the exponents in the prime factorization of numbers?

Published on 07 Apr 2026 - 9:46

score 429 · Answer 3 · 2026-03-28 22:24:20

429

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UFD implies GCD

Published on 28 Mar 2026 - 22:24

score 40 · Answer 4 · 2023-03-10 06:37:46

40

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Prove that if $\,kd\mid d\,$ then $\,k\leqslant1$

Published on 10 Mar 2023 - 6:37

score 126 · Answer 5 · 2023-03-14 03:53:37

126

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For any integer a, what integers are divisors of 0?

Published on 14 Mar 2023 - 3:53

score 27 · Answer 6 · 2026-04-01 04:23:20

27

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If $g \vert f,$ where $g=(X-1)^2,\ f=aX^{n+2}+bX^n+2,\ a,b\in\mathbb{R}$, determine $q(1)$, where $q\in\mathbb{R}[X]$ is the quotient of $f:g$

Published on 01 Apr 2026 - 4:23

score 68 · Answer 7 · 2023-03-14 18:17:27

68

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Is this method correct to find the remainder of $f(X^5):f(X)$, where $f=X^4+X^3+X^2+X+1$?

Published on 14 Mar 2023 - 18:17

score 135 · Answer 8 · 2023-03-15 05:54:54

135

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Find all positive number $n$ such that $n-1 \mid 1 + 10^n + 10^{2n}$

Published on 15 Mar 2023 - 5:54

score 94 · Answer 9 · 2026-04-06 01:09:03

94

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Prove $(n+1)^{m+1}-(-n)^{m+1}$ is divisible by $2n+1$

Published on 06 Apr 2026 - 1:09

score 134 · Answer 10 · 2023-03-26 01:36:46

134

Views

proof by induction that $4^n + 6n -1$ is a multiple of 9

Published on 26 Mar 2023 - 1:36

score 903 · Answer 11 · 2026-03-30 10:40:47

903

Views

How to prove that, among any +1 distinct odd integers from {1,…,3}, at least one will divide another?

Published on 30 Mar 2026 - 10:40

score 158 · Answer 12 · 2026-04-01 07:00:45

158

Views

Using the binomial theorem, show that $7^n +2$ is divisible by $3$

Published on 01 Apr 2026 - 7:00

score 110 · Answer 13 · 2026-04-07 12:47:51

110

Views

Negation of divisibility I cannot find the error

Published on 07 Apr 2026 - 12:47

score 257 · Answer 14 · 2023-04-05 00:08:30

257

Views

A question of Mayo Olympiad on permutations and multiple of 7

Published on 05 Apr 2023 - 0:08

score 199 · Answer 15 · 2023-04-07 11:46:45

199

Views

$4^{2^m}+6^{2^m}+9^{2^m}$ divides $4^{2^n}+6^{2^n}+9^{2^n}$

Published on 07 Apr 2023 - 11:46

List Question

order n polynomial long division question

What is the limiting mean value of the product of the exponents in the prime factorization of numbers?

UFD implies GCD

Prove that if $\,kd\mid d\,$ then $\,k\leqslant1$

For any integer a, what integers are divisors of 0?

If $g \vert f,$ where $g=(X-1)^2,\ f=aX^{n+2}+bX^n+2,\ a,b\in\mathbb{R}$, determine $q(1)$, where $q\in\mathbb{R}[X]$ is the quotient of $f:g$

Is this method correct to find the remainder of $f(X^5):f(X)$, where $f=X^4+X^3+X^2+X+1$?

Find all positive number $n$ such that $n-1 \mid 1 + 10^n + 10^{2n}$

Prove $(n+1)^{m+1}-(-n)^{m+1}$ is divisible by $2n+1$

proof by induction that $4^n + 6n -1$ is a multiple of 9

How to prove that, among any +1 distinct odd integers from {1,…,3}, at least one will divide another?

Using the binomial theorem, show that $7^n +2$ is divisible by $3$

Negation of divisibility I cannot find the error

A question of Mayo Olympiad on permutations and multiple of 7

$4^{2^m}+6^{2^m}+9^{2^m}$ divides $4^{2^n}+6^{2^n}+9^{2^n}$

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