Pletser, V. Linear Relations between Numbers of Terms and First Terms of Sums of Consecutive Squared Integers Equal to Squared Integers. Symmetry2024, 16, 146.
Pletser, V. Linear Relations between Numbers of Terms and First Terms of Sums of Consecutive Squared Integers Equal to Squared Integers. Symmetry 2024, 16, 146.
Pletser, V. Linear Relations between Numbers of Terms and First Terms of Sums of Consecutive Squared Integers Equal to Squared Integers. Symmetry2024, 16, 146.
Pletser, V. Linear Relations between Numbers of Terms and First Terms of Sums of Consecutive Squared Integers Equal to Squared Integers. Symmetry 2024, 16, 146.
Abstract
Sums of M consecutive squared integers (a+i)^2 equaling squared integers (for a<=1, 0<= i<= M-1) yield remarkable regular linear features when plotting values of M in function of a. These features correspond to groupings of pairs of a values for successive same values of M around straight lines of equation mu*M = 2a and are characterized in this paper for rational values of mu.
Keywords
Sums of consecutive squared integers equal to square integers; Quadratic diophantine equation; Generalized Pell equation; Fundamental solutions; Chebyshev polynomials
Subject
Computer Science and Mathematics, Algebra and Number Theory
Copyright:
This is an open access article distributed under the Creative Commons Attribution License which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
