london-journal-of-research-in-science-natural-and-formal London Journal of Research In Science: Natural and Formal 2631-8490 2631-8504 JournalsPress 64858 A Study on Two Curious Diophantine Problems 19 1 13 16

In this communication, an attempt has been made to obtain pairs of non-zero distinct integers such that, in each pair, i) The square of the sum added with the cube of the sum is equal to two times the sum of the cubes of the corresponding integers. ii) 2k times the square of the sum added with the cube of the sum is equal to two times the sum of the cubes of the corresponding integers.

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In this communication, an attempt has been made to obtain pairs of non-zero distinct integers such that, in each pair, i) The square of the sum added with the cube of the sum is equal to two times the sum of the cubes of the corresponding integers. ii) 2k times the square of the sum added with the cube of the sum is equal to two times the sum of the cubes of the corresponding integers.