On -adic zeros of systems of diagonal forms restricted by a congruence condition
Hemar Godhino, Paulo H. A. Rodrigues (2007)
Journal de Théorie des Nombres de Bordeaux
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This paper is concerned with non-trivial solvability in -adic integers of systems of additive forms. Assuming that the congruence equation has a solution with we have proved that any system of additive forms of degree with at least variables, has always non-trivial -adic solutions, provided . The assumption of the solubility of the above congruence equation is guaranteed, for example, if .