Quartic and Consecutive Concern (Posted on 2011-04-17)

N is an odd positive integer > 2 and each of a, b and c is a positive integer. It is known that; a, b and c (in this order), with a < b < c, corresponds to three consecutive terms of an arithmetic sequence such that:

N^{4} -1 = a*b*c

Prove that there are infinitely many solutions to the above equation.