On Sums of Seven Cubes

François Bertault (1) , Olivier Ramaré , Paul Zimmermann (1)

1 POLKA - Polynomials, Combinatorics, Arithmetic

We show that every integer between 1290741 and $3.375\,10^{12}$ is a sum of 5 non negative cubes from which we deduce that every integer which is a cubic residue modulo 9 and an invertible cubic residue modulo 37 is a sum of 7 non negative cubes.

Mots clés: waring's problem for cubes; conjecture de waring; computational number theory; sommes de puissances

Domaines: Autre [cs.OH]

François Bertault, Olivier Ramaré, Paul Zimmermann. On Sums of Seven Cubes. Mathematics of Computation, 1999, 68 (227), pp.1303-1310. ⟨inria-00108056⟩