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Modular Multiplicative Inverse
Find an exact modular inverse when it exists and download the gcd plus witnesses for the original integer inputs.
Signed decimal integers
JSON inverse and witness report
Browser only
Runs locally in your browser. Your files, pasted content and generated output are not uploaded. Reset clears this tool’s working data.
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How to use this tool
- Enter Integer a and Modulus m, with m at least 2.
- Select Find modular inverse.
- Download modular-inverse.json to inspect the exact inverse or no-inverse result and original-input witnesses.
Examples
For a=-3 and m=11, the inverse is 7 because (-3×7) modulo 11 equals 1.
Limitations
- 100 digits per integer, including leading zeros; 128 raw UTF-16 units per field; 1,000 Euclidean iterations, 512 intermediate digits, 64 KiB report and 30 seconds.
- Decimal integers only; modulus must be at least 2. Witness and inverse outputs are exact integer strings.
- No primality test, constant-time processing or cryptographic suitability claim.
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