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

Todorova, T. L.; Tolev, D. I.

doi:10.2478/tmmp-2014-0015

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.

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

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