Automorphic Numbers Calculator
Free online automorphic numbers calculator. Enter your values and get instant results with the formula, step-by-step working, a worked example and FAQs — everything runs locally in your browser on Calcton, no signup required.
中文版：自守数枚举计算器
原理：若 n² 的十进制末尾恰好是 n 本身（即 n² ≡ n (mod 10^d)，d 为 n 的位数），则称 n 为自守数。
步骤：输入上限 N，工具逐一检查 1 到 N 中每个数是否满足 n² 以 n 结尾。
示例：5² = 25、6² = 36、25² = 625、76² = 5776、376² = 141376、625² = 390625；≤1000 共 7 个：1, 5, 6, 25, 76, 376, 625。
注意事项：除 1 外自守数成对出现（末位为 5 与 6）；对每个位数 10^k，恰有两个非平凡自守数（如 9376 与 0625 型）；自守数与 76 型 5 幂级数、Idempotent 环结构相关。
参考值：376² = 141376；625² = 390625；≤10⁶ 共 11 个，最大 890625。
How to use the Automorphic Numbers Calculator
- Fill in the inputs with your own numbers — every field shows what it expects.
- The result updates instantly as you type; no "Calculate" click needed.
- Read the result card for the main figure, the step-by-step formula, and practical notes.
Frequently asked questions
Is the Automorphic Numbers Calculator free?
Yes — all math calculators on Calcton are free, with no sign-up required. Your inputs are processed in your browser and never sent to a server.
Is there a Chinese version of this tool?
Yes. Use the Chinese version link above — it is the same calculator with the interface in Simplified Chinese.
References
Formulas and benchmarks used by this calculator follow these published sources.
KevinContent LeadCalcton Editorial Team · Last updated 2026-10-01
Kevin maintains Calcton's formula verification and content: every calculator cites the standard it implements, worked examples are recomputed programmatically, and health benchmarks follow WHO and international guidelines.
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