Let p be a prime number. Let h(x) be a polynomial with integer coefficients such that h(0),h(1),\dots, h(p^2\minus{}1) are distinct modulo p2. Show that h(0),h(1),\dots, h(p^3\minus{}1) are distinct modulo p3. Putnamalgebrapolynomialmodular arithmeticfunctiongroup theorybinomial theorem