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

`(n+1)/(n+7)=(n+7-6)/(n+7)=1-\frac6{n+7}`


`n+7` will be a factor whenever the remainder term
`-\frac6{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?