# Math Help - Divisibility

1. ## Divisibility

There are given certain positive integer numbers $m,n,d$. Prove that if numbers $m^2n + 1$ and $mn^2 + 1$ are divisible by $d$, then numbers $m^3 + 1$ and $n^3 + 1$ are also divisible by $d$.

2. I don't have an answer, but for forum organization purposes this question was asked a week ago by someone else.

http://www.mathhelpforum.com/math-he...ty-154933.html

3. Originally Posted by PaulinaAnna
There are given certain positive integer numbers $m,n,d$. Prove that if numbers $m^2n + 1$ and $mn^2 + 1$ are divisible by $d$, then numbers $m^3 + 1$ and $n^3 + 1$ are also divisible by $d$.
Just play around with multiples of d and the result will fall out:

$m^2n+1 = pd,\quad mn^2+1 = qd,$

$m^2n^2 +n = npd,\quad m^2n^2+m = mqd,$

$n-m = (np-mq)d,$ and so $n = m+(np-mq)d,$

$m^2\bigl(m+(np-mq)d\bigr) + 1 = pd,$

$m^3+1 = (p-m^2np+m^3q)d.$