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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