# Sum of all positive integers : $\sqrt{7p^n+9}$

Find the sum of all positive integers which can be expressed as $\sqrt{7p^n+9}$ for some positive integer $n$ and some prime number $p$.

• Indeed, $45\ne49$. – Yves Daoust Jan 28 '17 at 14:46
• I think they have also added $\sqrt {7 (1)^n +9} =4$, but clearly $1$ is not prime. – Rohan Jan 28 '17 at 14:48
• I think, they knew that $p=1$ was not prime, and included $n=0$ (for some "non-negative integer", instead of "positive" integer). – Dietrich Burde Jan 28 '17 at 16:46