On the Equation x21 + x22 + x23 + x24 = N with Variables such that x1x2x3x4 + 1 is an Almost-Prime
e | 11 mar 2015
Tatra Mountains Mathematical Publications
Special Issue Title: Number Theory ‘14
INFORMAZIONI SU QUESTO ARTICOLO
Pubblicato online: 11 mar 2015
Pagine: 1 - 26
Ricevuto: 22 giu 2014
DOI: https://doi.org/10.2478/tmmp-2014-0015
© 2015
This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 3.0 License.
We consider Lagrange’s equation x21 +x22 +x23 +x24 = N, where N is a sufficiently large and odd integer, and prove that it has a solution in natural numbers x1, . . . , x4 such that x1x2x3x4 + 1 has no more than 48 prime factors.