Celebrating my comeback with "Primes" ^_^

Number Theory Level 4

Find the sum of all prime numbers \(p\) which satisfy \[\displaystyle p \mid 17^p + 31^{2p} + 19^{3p} \]

Details and Assumptions :-

\(\bullet\) \(a \mid b\) means "\(a\) divides \(b\)" i.e. \(b\) is divisible by \(a\).

\(\bullet\) A prime number is a positive integer which has only 2 positive integer divisors, \(1\) and itself.


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