Integer Reciprocals with Pandigital Reptends
2025-04-24
This article investigates the existence of integers whose reciprocals have a decimal representation with a recurring block of digits containing all ten decimal digits. It's shown that such integers exist (e.g., 72728). The article extends this to other bases, proving no such integers exist for odd bases. Computer searches have ruled out some even bases, but the general problem remains open. The exploration delves into number theory and group theory, providing a theoretical framework for solving this intriguing mathematical puzzle.
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