On the Equation x 2 1 + x 2 2 + x 2 3 + x 2 4 = N with Variables such that x 1 x 2 x 3 x 4 + 1 is an Almost-Prime

Tatyana Todorova; D. I. Tolev

doi:10.2478/tmmp-2014-0015

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On the Equation x ² ₁ + x ² ₂ + x ² ₃ + x ² ₄ = N with Variables such that x ₁ x ₂ x ₃ x ₄ + 1 is an Almost-Prime

Tatyana Todorova D. I. Tolev

Year: 2014 Journal: Tatra Mountains Mathematical Publications Vol: 59 (1)Pages: 1-26 Publisher: De Gruyter

DOI: 10.2478/tmmp-2014-0015

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Abstract

Abstract We consider Lagrange’s equation x 2 1 +x 2 2 +x 2 3 +x 2 4 = N, where N is a sufficiently large and odd integer, and prove that it has a solution in natural numbers x 1 , . . . , x 4 such that x 1 x 2 x 3 x 4 + 1 has no more than 48 prime factors.

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Mathematics Combinatorics Integer (computer science)

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On the Equation x ² ₁ + x ² ₂ + x ² ₃ + x ² ₄ = N with Variables such that x ₁ x ₂ x ₃ x ₄ + 1 is an Almost-Prime

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