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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