# Maximizing the Sum of Pairs Satisfying an Equation

**Number Theory**Level 4

Consider all positive integer solutions \((x_i,y_i)\) to

\[1+2^x+2^{2x+1}=y^2\]

Find the maximum value of the sum \(x_i+y_i\).

Consider all positive integer solutions \((x_i,y_i)\) to

\[1+2^x+2^{2x+1}=y^2\]

Find the maximum value of the sum \(x_i+y_i\).

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