Problem of the Day
Let be a positive integer. Is divisible by ?
(2) is primeReveal Answer
D. Each statement alone is sufficient.See the Solution
Note that $n^2-1$ is always divisible by $n+1$ because $n^2-1=(n+1)(n-1)$. In other words, $n^2-1$ is a multiple of $n+1$. The number $n^2+1$ is only $2$ more than $n^2-1$ and hence cannot also be a multiple of $n+1$ unless $n=1$.
Statement 1: SUFFICIENT. This tells us that $n$ is definitely not 1, which means $n^2+1$ cannot be divisible by $n+1$
Statement 2: SUFFICIENT. If $n$ is prime it cannot be $1$.
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