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I think there is a mistake in the question. Because as per the condition, x is the number of elements of the set {-(p-1),-(p-2),…(p-2),(p-1)}. So it means x = 2p-1. But again, 2x^2 + 2x + 1 is divisible by p. From these conditions the only suitable value of p is 1. But p is prime. So there are no values of p that satisfy x. Thus, no value of Sp.. I’m confused.
the number of elements is S_p