Number Theory F in Z[x]...

From: Alex.Lupas (alexandru.lupas_at_ulbsibiu.ro)
Date: 10/14/04 

Date: 13 Oct 2004 21:39:51 -0700

Let F(x)=x^n+ n-1 and consider the statement:
 
 ,,There are an infinite number of positive integres m such that
   
  F(m) has at most k, k=k(n)= k(F,n), prime factors."

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Question: What about k= k(n) ? Upper bounds,... ?
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Some known results :
a) k(2)= 5 - B.V.Levin -[1960]
b) k(3)= 4 - Y. Wang - [1957]
Other information: In case when G(x)=x(x+2), A.Selberg-[1947] has
proved that k(G,n)=5.