Find all nonnegative integers $a$ and $b$ that satisfy the equation $$3 \cdot 2^a + 1 = b^2.$$
Problem
Source: OLCOMA Costa Rica National Olympiad, Final Round, 2016 Shortlist N3 day1
Tags: number theory, Diophantine equation, diophantine
Source: OLCOMA Costa Rica National Olympiad, Final Round, 2016 Shortlist N3 day1
Tags: number theory, Diophantine equation, diophantine
Find all nonnegative integers $a$ and $b$ that satisfy the equation $$3 \cdot 2^a + 1 = b^2.$$