# What's with the restriction on \(p\)?

**Number Theory**Level 5

Find the number of solution triples \((p, a, b)\) to the equation

\(\sqrt{a} + \sqrt{a + 8p} = 4 + 2^{b}\)

where \(a\) and \(b\) are positive integers and \(p \lt 100000\) is prime.

Find the number of solution triples \((p, a, b)\) to the equation

\(\sqrt{a} + \sqrt{a + 8p} = 4 + 2^{b}\)

where \(a\) and \(b\) are positive integers and \(p \lt 100000\) is prime.

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