MathDB

Let

n

denote the product of the first

2013

primes. Find the sum of all primes

p

with

20 \le p \le 150

such that (i)

\frac{p+1}{2}

is even but is not a power of

2

, and (ii) there exist pairwise distinct positive integers

a,b,c

for which

a^n(a-b)(a-c) + b^n(b-c)(b-a) + c^n(c-a)(c-b)

is divisible by

p

but not

p^2

.
Proposed by Evan Chen

Problem Statement