Let p be an odd prime number and define v(p) as the number of triples of consecutive numbers in 1,2,..., p 1 in which the three of them are quadratic residues modulo p. For example, modulo p = 7 we know that the quadratic residues are 1, 2 and 4. Hence, v(7) = 0. For another example, consider modulo p = 19. The quadratic residues are highlighted with red: 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18 The triples of three consecutive quadratic residues modulo 19 are: (4,5,6) and (5, 6, 7). Hence (19) = 2. In lecture we will prove that |- (1) - 1 | < VP 4 inequalities. In this problem we study related (a) (3 points) Let N stand for non-quadratic residue and R stand for quadratic residue. For any sequence XYZ, where X, Y, Z are either N or R, define xyz (p) as the number of consecutive integer triples in 1, 2, ..., p-1 such that their quadratic nature is given in order by X, Y and Z. For example, v(p) = VRRR(P). Prove that the same inequality holds for any choice of X, Y, Z. That is, prove P VXYZ