Find all pairs of nonnegative integers $(a, b)$ such that $a+2b-b^2=\sqrt{2a+a^2+|2a+1-2b|}$.
Problem
Source: 2011 Saudi Arabia Pre-TST February 3.2
Tags: Diophantine equation, diophantine, number theory
Source: 2011 Saudi Arabia Pre-TST February 3.2
Tags: Diophantine equation, diophantine, number theory
Find all pairs of nonnegative integers $(a, b)$ such that $a+2b-b^2=\sqrt{2a+a^2+|2a+1-2b|}$.