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Diophantine Equation Solutions Analysis by Manasi Sahukar is a document available to read on EtoBox.

This paper revisits the Diophantine equation (x + 1)k + (x + 2)k + · · · + (`x)k = y n for fixed integers k, ` ≥ 2, proving that all integer solutions with x, y ≥ 1 and n ≥ 2 satisfy max{x, y, n} < C, where C is a computable constant depending on k and `. The authors build on previous work and provide a comprehensive analysis of the equation, particularly for cases when k is not equal to 3 and ` is odd. The findings contribute to the understanding of the solutions to this class of equations in number theory

Author

Manasi Sahukar

Language

EN