Journal Title/Source

Alabama Journal of Mathematics

Publication Date

2026

Volume

49

Page Numbers

34-38

Document Type

Journal Article

Department

Mathematics and Computer Science

Abstract

We find all non-negative integers n such that congruence modulo n is stable under exponentiation by positive integers, i.e. we show, that n = 1, 2, 6, 42, 1806 are the only numbers for which the condition a ≡n b and c ≡n d imply that a c ≡n b d , a, b, c, d ∈ N is satisfied. We also show in what sense this condition is close to the conditions for Carmichael numbers.

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