Question

There are exactly four positive integers n such that (n +7) is a factor of ( n +1) . Find the largest such n .

Answer 1

$\dfrac{n+1}{n+7}=\dfrac{n+7-6}{n+7}=1-\dfrac6{n+7}$

$n+7$ will be a factor whenever the remainder term $-\dfrac6{n+7}$ vanishes. But this will never happen for any integer $n$, so I suspect the question is inaccurately posed. Are there some characters missing?