Abstract
The paper contains an investigation of conditions under which
R
simultaneous equations of additive type in
N
unknowns have a solution in integers, not all 0. If the degree
k
of the equations is odd, it suffices if
N
is greater than an explicit function of
R
and
k
. If
k
is even, two further conditions are imposed, and neither can be entirely avoided. It is also proved that the equations have a solution in
p
-adic integers, not all 0, if
N
is greater than an explicit function of
R
and
k
.
Cited by
48 articles.
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