Question 190
Find all primes $p$ and $q$, and even numbers $n\gt 2$, satisfying the equation
$$
p^{n}+p^{n-1}+\cdots+p+1=q^{2}+q+1
$$
$$
p^{n}+p^{n-1}+\cdots+p+1=q^{2}+q+1
$$
MathNet 2003 — Part 01 Question 190
Math Olympiad Vault · MathNet 2003 — Part 01