Theorem reveals conditions for A^n + B^n - C^n = 0 in natural numbers, suggesting new insights into prime base systems.
Theorem. In a hypothetical equality A n + B n - C n = 0 in a number system with a prime base n > 2, mutually prime natural numbers A, B, C (mod n k ) starting from k=1 equal to the numbers A 1 n^(k-1) , B 1 n^(k-1) , C 1 n^(k-1) (mod n k ), where k can be arbitrarily large.
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Victor Sorokine (2025) studied this question.
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