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.
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