Understand the problem
Source of the problem
Start with hints
(modp). Now p can be 3. For p = 3, Observe that a = 1 and b = 2 is a solution. Now if p is not 3, then p must divide a and b. This implies a + b must be greater than equal to 2p, hence contradiction.
Hence the solutions are a = 1, b =1, p = 2
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