Skip to main content
Internet Archive's 25th Anniversary Logo

Full text of "Proposed Problem (4)"

See other formats


Let m be a fixed positive integer. Calculate: 

a m 
Lim n (P. ) / P, 

L —> Co 

where n(n) is Smarandache Function defined as the smallest integer 

m such that m! is divisible by n, and p. the prime series. 

k , 

We note by Ps a prime number greater than m. We show that 
m . ‘ 
1 {P. ) = mp., for any i > 3 
t by absurd q (p,” ) =ąa< mp, then 
a! =1°2- e.t DS ara (2p)... ° ((M=K) DO) * ya a, with k > 0, will 
(5 & 
eee A mak m 
divisible by P; Dut not by Pe > 

Then this limit is equal tom. 

Pedro Melendez 

Av. Cristovao Colombo 336 
30.000 Belo Horizonte, MG