A PROBLEM CONCERNING THE FIBONACCI RECURRENCE (6) by T. Yau, student, Pima Community College

"Let S(n) be defined as the smallest integer such that (S(m))! is divisible by n (Smarandache Function). For what triplets this function verifies the Fibonacci relationship, i.e. find n such that

S(n) + S(n+l) = S(n+2) ?

solution: Checking the first 1200 numbers, I found just two triplets for which this function verifies the Fibonacci relationship:

S(9) + $(10) = S(11) © 6+ 5 = 11, and S(i19). + S(120) = S(121) © 17 + 5 = 22. "How many other triplets with the same property do exist ? (I can’t find a theoretical proof ...) Reference:

M. Mudge, "Mike Mudge pays a return visit to the Fl rentin Smarandache Function", in <Personal Computer World>, London, February 1993, p. 403.