List questions from divisibility

Published on 22 Jan 2019 - 23:21

48

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Prove that, for all $n\in{Z}$, if $3\mid{n}$ or $18\mid{n-7}$, then there exists $m\in{Z}$ such that $(n^2-9m)(n-9m+2)=0$.

Published on 23 Jan 2019 - 2:05

109

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Is the number $x^9+2x^7+3x^3+4x$ divisible for 5?

Published on 24 Jan 2019 - 14:46

129

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Find $n$ such that polynomial is divisible

Published on 24 Jan 2019 - 15:35

59

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Under which conditions is $\gcd(a+bx,c)=1$ solvable and what is the solution?

Published on 26 Mar 2026 - 14:43

183

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Prove (or disprove) that $3^{2n+3}+40n-27$ is divisible by $64$ for any $n$ integer

Published on 25 Jan 2019 - 23:48

127

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Definition of prime numbers and equivalence

Published on 26 Jan 2019 - 10:59

76

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Is the sum of the first $2n+1$ primes ever divisible by 3?

Published on 27 Jan 2019 - 1:37

69

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Prove $\gcd(a,m) \mid \gcd(ab,m)$ $\forall a,b,m \in \Bbb Z$

Published on 26 Mar 2026 - 14:43

76

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Various questions from a discrete mathematics course

Published on 27 Jan 2019 - 15:07

103

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If $12\mid{a}$ then $4\nmid{b}$ or $4\mid{(8+2a+5b)}$.

Published on 27 Jan 2019 - 22:21

175

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Product of n integers of AP is divisible by $n!$

Published on 29 Jan 2019 - 7:45

99

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Either $np$ is even, or $n^2 − p^2$ is a multiple of $8$.

Published on 25 Mar 2026 - 12:19

69

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How to prove b | a iff remainder = 0

Published on 30 Jan 2019 - 16:38

31

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System of divisibility constraints

Published on 25 Mar 2026 - 15:40

List Question

What does it mean to not divide any term

Prove that, for all $n\in{Z}$, if $3\mid{n}$ or $18\mid{n-7}$, then there exists $m\in{Z}$ such that $(n^2-9m)(n-9m+2)=0$.

Is the number $x^9+2x^7+3x^3+4x$ divisible for 5?

Find $n$ such that polynomial is divisible

Under which conditions is $\gcd(a+bx,c)=1$ solvable and what is the solution?

Prove (or disprove) that $3^{2n+3}+40n-27$ is divisible by $64$ for any $n$ integer

Definition of prime numbers and equivalence

Is the sum of the first $2n+1$ primes ever divisible by 3?

Prove $\gcd(a,m) \mid \gcd(ab,m)$ $\forall a,b,m \in \Bbb Z$

Various questions from a discrete mathematics course

If $12\mid{a}$ then $4\nmid{b}$ or $4\mid{(8+2a+5b)}$.

Product of n integers of AP is divisible by $n!$

Either $np$ is even, or $n^2 − p^2$ is a multiple of $8$.

How to prove b | a iff remainder = 0

System of divisibility constraints

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