# Petar's equations

Algebra Level 5

Consider the system of equations:

\begin{align} xa + y\sin \left(\pi \sqrt{a^2+b^2}\right) & = 0 \\ xb + y\sin \left(\pi \sqrt{a^2+b^2}\right) &= 0 . \end{align}

How many different ordered pairs of integers $$(a, b)$$ subject to $$\left| a \right| < 6, \left| b \right| < 6$$ are there such that the equations have a non-trivial solution $$(x,y)$$?

This problem is posed by Petar V.

Details and assumptions

A non-trivial solution is a pair of values $$(x,y) \neq (0,0)$$ which satisfies both equations.

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