30 Sep
2008
30 Sep
'08
10:16 p.m.
Puzzle: While futzing around with "prime formulas", I noticed that 8^8 - 7^7 = 3 * 19 * 19 * 14731, and then 14^14 - 13^13 = 3 * 61 * 61 * 968299894201. This clue leads to the following guess: When N = 6K+1, (N^2+N+1)^2 | 3 * [(N+1)^(N+1) - N^N]; and When N = 6K+4, (N^2+N+1)^2 | 3 * [(N+1)^(N+1) + N^N]. For example, N=16: 273^2 | 3 * (17^17 + 16^16). True or False? Rich