Sums of Positive Integer Powers with Unlike Exponents - Garista, Eugenio; Zanoni, Alberto (Armenian Journal of Mathematics, 2025)
Consider the following problem: given a positive integer, what is the minimum number of positive integer powers having unlike exponents greater than one such that their sum is equal to the given number? We deal with this open question by presenting some experimental results, indicating some inequalities and relations, presenting some new integer sequences, obtaining a bivariate generating function, and eventually proposing a conjecture.