AN INFINITE FAMILY OF QUARTIC POLYNOMIALS WHOSE PRODUCTS OF CONSECUTIVE VALUES ARE FINITELY OFTEN PERFECT SQUARES

摘要

Using an elementary identity, we prove that for infinitely many polynomials P(x) 2 Z[X] of fourth degree, the equation Qn k=1 P(k) = y2 has finitely many solutions in Z. We also give an example of a quartic polynomial for which the product of its consecutive values is infinitely often a perfect square.