Universal Balance Law - Fundamental Advance in Power-Sum Balancing

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Saša Mb

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Aug 23, 2025, 2:00:57 AMAug 23

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Dear Sequence Fans,

I have developed a method (Universal Balance Law) that constructs two distinct blocks of integers with equal sums of like powers for all natural exponents infinite families of solutions).

Unlike classical Prouhet-type solutions requiring blocks of size 2^m, this method works also for unequal block sizes (e.g., 23 vs. 24 terms for ):

This also works for irrationals, transcendental and complex numbers (deterministic with integer / rational coefficients).

The most elegant solutions, of course, are those in integers. UBL provides infinite solutions even for distinct consecutive integer sequences of different lengths in each block (I can share examples upon request).

Is this known? I would appreciate references or thoughts.

Core question:

Is there a known systematic method that achieves this universally?
If not, UBL resolves a fundamental gap..