Math & Numbers

Extended Euclidean Algorithm (ax + by = gcd(a, b))

Bézout coefficients for any-sign integers with the full division-step table, lcm, and optional linear Diophantine solving (particular + general solution).

text· Text resultOpen tool

Quick start

Call this tool from your code in three languages.

cURL

curl -X POST 'https://api.elysiatools.com/en/api/tools/extended-euclidean-algorithm' \
  -H 'Content-Type: application/json' \
  -d '{"a":"240","b":"46","c":"e.g. 4 — leave empty for the plain Bézout identity","style":"steps"}'

API reference

Send a POST request with your inputs as JSON. File parameters require a separate upload first.

Endpoint

HTTP

POST https://api.elysiatools.com/en/api/tools/extended-euclidean-algorithm

Parameters

Name	Type	Required	Description
a	text	Yes	First integer; negative values are supported.
b	text	Yes	Second integer; negative values are supported.
c	text	No	Optional target: solves ax + by = c when gcd(a, b) divides c.
style	select	Yes	—

Response format

Text result

JSON

{
  "result": "Processed text content",
  "error": "Error message (optional)",
  "message": "Notification message (optional)",
  "metadata": {
    "key": "value"
  }
}

MCP integration

Add this tool to your Model Context Protocol server so AI agents can list and call it.

Server configuration

Add this block to your MCP client configuration:

mcp.json

{
  "mcpServers": {
    "elysiatools-extended-euclidean-algorithm": {
      "name": "extended-euclidean-algorithm",
      "description": "Bézout coefficients for any-sign integers with the full division-step table, lcm, and optional linear Diophantine solving (particular + general solution).",
      "baseUrl": "https://api.elysiatools.com/mcp/sse?toolId=extended-euclidean-algorithm",
      "command": "",
      "args": [],
      "env": {},
      "isActive": true,
      "type": "sse"
    }
  }
}

List available tools

After connecting to the SSE endpoint, list the exposed tools:

tools/list

{
  "jsonrpc": "2.0",
  "id": 1,
  "method": "tools/list"
}

Call this tool

Invoke the tool by its id, passing arguments built from its parameters:

tools/call

{
  "jsonrpc": "2.0",
  "id": 2,
  "method": "tools/call",
  "params": {
    "name": "extended-euclidean-algorithm",
    "arguments": {
  "a": "240",
  "b": "46",
  "c": "e.g. 4 — leave empty for the plain Bézout identity",
  "style": "steps"
}
  }
}

Chain multiple tools in one session with a comma-separated toolId list, e.g. /mcp/sse?toolId=png-to-webp,jpg-to-webp,gif-to-webp (max 20).

Questions or issues? Contact [email protected]

Browse tools Open tool

curl -X POST 'https://api.elysiatools.com/en/api/tools/extended-euclidean-algorithm' \ -H 'Content-Type: application/json' \ -d '{"a":"240","b":"46","c":"e.g. 4 — leave empty for the plain Bézout identity","style":"steps"}'

Name

Type

Required

Description

text

Yes

First integer; negative values are supported.

text

Yes

Second integer; negative values are supported.

text

Optional target: solves ax + by = c when gcd(a, b) divides c.

style

select

Yes

—

{ "mcpServers": { "elysiatools-extended-euclidean-algorithm": { "name": "extended-euclidean-algorithm", "description": "Bézout coefficients for any-sign integers with the full division-step table, lcm, and optional linear Diophantine solving (particular + general solution).", "baseUrl": "https://api.elysiatools.com/mcp/sse?toolId=extended-euclidean-algorithm", "command": "", "args": [], "env": {}, "isActive": true, "type": "sse" } } }

{ "jsonrpc": "2.0", "id": 2, "method": "tools/call", "params": { "name": "extended-euclidean-algorithm", "arguments": { "a": "240", "b": "46", "c": "e.g. 4 — leave empty for the plain Bézout identity", "style": "steps" } } }