Integer mod inverse

integer-mod-inverse · version 1.0.0 · Numbers & math · free, no key needed

Compute the modular multiplicative inverse of a modulo modulus, when it exists.

Use when you need to: integer mod inverse · modular multiplicative inverse · modular inverse.

Supported

• integer mod inverse
• modular multiplicative inverse
• modular inverse
• inverse mod m

Not supported

• modular exponentiation
• extended gcd output
• inverse when gcd is not 1

Behavior

• a and modulus are canonical integer strings; modulus must be a positive canonical integer.
• a may be negative or exceed modulus; it is reduced modulo modulus before inverting.
• The inverse exists only when gcd(a mod modulus, modulus) = 1; otherwise the request is rejected as undefined.
• modulus 1 is a degenerate ring where every residue is 0; this contract returns value 0 for modulus 1.
• The result is the unique value in [0, modulus) such that (a * value) mod modulus = 1 (or 0 when modulus is 1).
• Each input may have at most 1000 digits excluding sign.

Input

• a (string, required): min length 1; max length 1001
• modulus (string, required): min length 1; max length 1001

Output

• value (string, required)

Limits

• max digits: 1000

Example

Request input:

{
  "a": "3",
  "modulus": "11"
}

Response:

{
  "result": {
    "value": "4"
  }
}

How to call it

MCP

Connect https://computefirst.net/mcp (setup), then call execute with:

{
  "id": "integer-mod-inverse",
  "version": "1.0.0",
  "input": {
    "a": "3",
    "modulus": "11"
  }
}

HTTP (no key)

curl -X POST https://computefirst.net/v1/tools/integer-mod-inverse/versions/1.0.0/execute \
  -H "Content-Type: application/json" \
  -d '{"a":"3","modulus":"11"}'

The machine-readable contract is at /v1/tools/integer-mod-inverse/versions/1.0.0.

CLI

node cli.mjs run integer-mod-inverse 1.0.0 --input input.json --base-url https://computefirst.net

Get the client at /clients/cli/.

Related tools

• Integer mod pow: Compute base^exponent mod modulus exactly using fast modular exponentiation.
• Integer CRT: Solve a system of integer congruences (x ≡ remainder mod modulus) with the Chinese Remainder Theorem.
• Rational reciprocal: Invert a rational number given as a numerator/denominator integer-string pair.
• Array integer adjacent diff: Replace an array of canonical integer strings with consecutive first differences.
• Array integer clamp: Clamp an array of canonical integer strings to optional inclusive min and max bounds.
• Array integer cumulative sum: Replace an array of canonical integer strings with equal-length prefix sums.