PROPOSED PROBLEM (4)
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 ,
Solution:
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
BRAZIL
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be