JP Journal of Algebra, Number Theory and Applications
Volume 14, Issue 1, Pages 37 - 50
(June 2009)
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ON A GENERALIZATION OF D. H. LEHMER PROBLEM
Yi Yuan (P. R. China) and Hou Yiwei (P. R. China)
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and
it
is clear that there exists one and only one
with
such
that
Let
k be any fixed integer with
denote the number of all k‑tuples
with positive integer coordinates
such
that
and
If
is
an odd prime and
is an even number, then we let
denote
the number of all k-tuples with primitive roots coordinates
such
that
and
The
main purpose of this paper is to use the estimates of general Kloosterman’s
sums and the properties of trigonometric sums to study the asymptotic behavior
of the mean values
and
and
to give two interesting asymptotic formulae.