# A number theory problem by Priyanshu Mishra

Number Theory Level 5

Suppose that $$a$$ and $$b$$ are positive integers such that

$\large\ p=\frac { b }{ 4 } \sqrt { \frac { 2a-b }{ 2a+b } }$

is a prime number. What is the maximum possible value of $$p$$?

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