Integer extended GCD

integer-extended-gcd · version 1.0.0 · Numbers & math · free, no key needed

Compute the extended Euclidean algorithm result: gcd(a, b) and Bezout coefficients x, y with a*x + b*y = gcd.

Use when you need to: integer extended gcd · extended euclidean algorithm · bezout coefficients.

Supported

• integer extended gcd
• extended euclidean algorithm
• bezout coefficients
• bezout identity

Not supported

• plain gcd without coefficients
• lcm
• modular inverse of a non-coprime pair

Behavior

• Inputs are canonical integer strings: 0 or an optional ASCII minus followed by a non-zero leading digit.
• The input -0 is accepted and canonicalized to 0 before evaluation.
• a = 0 and b = 0 together are rejected: the gcd is undefined.
• gcd is the non-negative greatest common divisor of a and b.
• x and y are Bezout coefficients satisfying a*x + b*y = gcd exactly, using the original signed a and b.
• x and y are not unique; this contract returns the pair produced by the standard iterative extended Euclidean algorithm.
• Each input and each output field may have at most 1000 digits excluding sign.

Input

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

Output

• gcd (string, required)
• x (string, required)
• y (string, required)

Limits

• max digits: 1000

Example

Request input:

{
  "a": "35",
  "b": "15"
}

Response:

{
  "result": {
    "gcd": "5",
    "x": "1",
    "y": "-2"
  }
}

How to call it

MCP

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

{
  "id": "integer-extended-gcd",
  "version": "1.0.0",
  "input": {
    "a": "35",
    "b": "15"
  }
}

HTTP (no key)

curl -X POST https://computefirst.net/v1/tools/integer-extended-gcd/versions/1.0.0/execute \
  -H "Content-Type: application/json" \
  -d '{"a":"35","b":"15"}'

The machine-readable contract is at /v1/tools/integer-extended-gcd/versions/1.0.0.

CLI

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

Get the client at /clients/cli/.

Related tools

• Array integer GCD: Compute the non-negative greatest common divisor of an array of canonical integer strings.
• Integer GCD: Compute the non-negative greatest common divisor of two canonical integer strings.
• 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.
• Array integer LCM: Compute the non-negative least common multiple of an array of canonical integer strings.