Prove: (F_mn-1) - (F_n-1)^m is divisible by (F_n)² for all m≥1 and n>1.

Jer, your counter-example for the usual system seems to have a problem with it. In the standard numbering format for the sequence, F5 = 5, whereas you have considered it to be equal to 8. Setting F5 to the correct value of 5:

(F5) - (F2)^2 = 5 - 1^2 = 4 which IS divisible by (F3)^2 = 2^2 = 4.

Posted by Justin on 2013-07-06 23:33:26