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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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