List questions from divisibility

Published on 12 Apr 2026 - 7:43

47

Views

Suppose $m/l$ is a root of $f$, where $m$ and $l$ are relatively prime integers. Show that $m$ divides $a_0$ and $l$ divides $a_n$.

Published on 15 Apr 2026 - 23:19

36

Views

Factors/divisibility of monotonically-increasing integer polynomial

Published on 13 Apr 2026 - 1:08

1.5k

Views

Show that $\gcd(a,b)=d\Rightarrow\gcd(a^2,b^2)=d^2\ $

Published on 13 Apr 2026 - 16:24

1.1k

Views

Show that among every consecutive 5 integers one is coprime to the others

Published on 15 Apr 2026 - 10:01

48

Views

Show that $\gcd(80,8a^2+1)=1$

Published on 16 Apr 2026 - 9:33

81

Views

Need an assistance with a specific step of a specific Division Algorithm proof

Published on 11 Apr 2026 - 18:29

366

Views

How to prove $p^2 \mid \binom {2p} {p }-2$ for prime $p$?

Published on 13 Apr 2026 - 14:02

101

Views

Finding the integers

Published on 12 Apr 2026 - 23:48

87

Views

When does $a^b\mid b^a$

Published on 12 Apr 2026 - 3:19

40

Views

Get first digits of a very large quotient

Published on 31 Mar 2026 - 17:50

129

Views

Is it divisible by $3^n$?

Published on 08 Apr 2026 - 17:08

813

Views

Proof using deductive reasoning

Published on 12 Apr 2026 - 17:43

297

Views

Prove that n is a multiple of four....

Published on 12 Apr 2026 - 14:18

4.5k

Views

How many numbers less than 100 have the sum of factors as odd?

Published on 12 Apr 2026 - 15:38

List Question

Digit-sum division check in base-$n$

Suppose $m/l$ is a root of $f$, where $m$ and $l$ are relatively prime integers. Show that $m$ divides $a_0$ and $l$ divides $a_n$.

Factors/divisibility of monotonically-increasing integer polynomial

Show that $\gcd(a,b)=d\Rightarrow\gcd(a^2,b^2)=d^2\ $

Show that among every consecutive 5 integers one is coprime to the others

Show that $\gcd(80,8a^2+1)=1$

Need an assistance with a specific step of a specific Division Algorithm proof

How to prove $p^2 \mid \binom {2p} {p }-2$ for prime $p$?

Finding the integers

When does $a^b\mid b^a$

Get first digits of a very large quotient

Is it divisible by $3^n$?

Proof using deductive reasoning

Prove that n is a multiple of four....

How many numbers less than 100 have the sum of factors as odd?

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