[math-fun] Toe-curling classical number-theory problem

The following kept me at bay for an embarrassing length of time, despite my conviction that there just had to be a simple, one --- well, maybe three --- line proof (there is). Question (elementary): for p odd prime, show that the order of any element of PGL(2, p) divides some member of {p-1, p, p+1} . Rider (harder): locate where the @£$%^&* this might be concealed amidst the 330-odd densely obfuscated pages of L. E. Dickson (1901, 1958) "Linear groups with an exposition of the Galois field theory" Some things were quite definitely not better in the old days! Fred Lunnon