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

Todorova, T. L.

and

Mar 11, 2015

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

Tatra Mountains Mathematical Publications

Volume 59 (2014): Issue 1 (June 2014)

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Published Online: Mar 11, 2015

Page range: 1 - 26

Received: Jun 22, 2014

DOI: https://doi.org/10.2478/tmmp-2014-0015

Keywords
Lagrange’s equation, almost-primes

© 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.

Language:: English

Publication timeframe:: 3 times per year
Journal Subjects:: Mathematics, General Mathematics

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