<abstract xmlns="http://www.w3.org/1999/xhtml">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.</abstract>

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.

On the Equation x21 + x22 + x23 + x24 = N with Variables such that x1x2x3x4 + 1 is an Almost-Prime

Faculty of Mathematics and Informatics Sofia University “St. Kl. Ohridsky” 5 J. Bourchier 1164 Sofia BULGARIA

Institute of Mathematica and Informatics, BAS 8 Acad. G. Bonchev 1113 Sofia BULGARIA

Tatra Mountains Mathematical Publications

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On the Equation x + x + x + x = N with Variables such that xxxx + 1 is an Almost-Prime

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...

On the Equation x²₁ + x²₂ + x²₃ + x²₄ = N with Variables such that x₁x₂x₃x₄ + 1 is an Almost-Prime

Published Online: Mar 11, 2015

Page range: 1 - 26

Received: Jun 22, 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.