n is an odd positive integer > 2 and each of x, y, and z is a positive integer. It is known that x, y and z (in this order), with x < y < z, correspond to three consecutive terms of an arithmetic sequence such that n^k-1=x*y*z.

Prove (1) that there are infinitely many solutions to the above equation for every positive integer k;
(2) that there is a solution for every n, if k is even.

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