Let n≥3 be a positive integers and p be a prime number such that p>6n−1−2n+1. Let S be the set of n positive integers with different residues modulo p. Show that there exists a positive integer c such that there are exactly two ordered triples (x,y,z)∈S3 with distinct elements, such that x−y+z−c is divisible by p. number theoryprime numbers