JP Journal of Algebra, Number Theory and Applications
Volume 4, Issue 1, Pages 55 - 78
(April 2004)
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ON PAIRS OF ADDITIVE CONGRUENCES OF ODD DEGREE
H. Godinho (Brasil), J. F. Lima Neto (Brasil), P. H. A. Rodrigues (Brasil)
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Abstract: Here we present some
conditions for pairs of additive congruences
of odd degree to have non-trivial solutions
and non-singular solutions modulo a prime p.
For non-trivial solutions it is proved that
pairs of additive congruences in n variables
and odd degree d
and have
common non-trivial zeros provided
Later we consider pairs of additive forms of
odd degree d
and in n
variables over p-adic fields and
prove that one can guarantee p-adic
common zeros provided |
Keywords and phrases: homogeneous
polynomials, Artin’s conjecture, p-adic
forms. |
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