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Automorphic number - mklabgr - 07-05-2026
Automorphic number
Summary
An automorphic number is a number that has a curious self-reproducing property: when you square it, the result ends in the same digits as the original number. For example, 5² = 25, so 5 appears at the end, and 76² = 5776, so 76 repeats at the end as well. This idea is studied in basic number theory and is mostly about patterns in the decimal system rather than deep applications.
What makes these numbers interesting is that they feel almost “self-aware” in how they reappear inside their own square. Mathematicians also study how many such numbers exist in different bases and how their structure connects to modular arithmetic, but at its core, it’s a simple and elegant digit pattern phenomenon in arithmetic.
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