Math & Numbers

Modular Arithmetic Calculator (Add / Subtract / Multiply / Inverse / Power)

Exact BigInt modular arithmetic for values up to 10¹⁸: (a ± b) mod m, (a × b) mod m, a⁻¹ mod m via extended Euclid, and aᵇ mod m via fast exponentiation.

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/modulo-arithmetic-converter' \
  -H 'Content-Type: application/json' \
  -d '{"operation":"power","a":"17","b":"5","m":"13"}'

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/modulo-arithmetic-converter

Parameters

Name	Type	Required	Description
operation	select	Yes	—
a	text	Yes	First operand (the base in power mode, the value being inverted in inverse mode).
b	text	No	Second operand — the exponent in power mode; unused in inverse mode.
m	text	Yes	Modulus, m ≥ 2. Results are reduced to the canonical range [0, m−1].

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-modulo-arithmetic-converter": {
      "name": "modulo-arithmetic-converter",
      "description": "Exact BigInt modular arithmetic for values up to 10¹⁸: (a ± b) mod m, (a × b) mod m, a⁻¹ mod m via extended Euclid, and aᵇ mod m via fast exponentiation.",
      "baseUrl": "https://api.elysiatools.com/mcp/sse?toolId=modulo-arithmetic-converter",
      "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": "modulo-arithmetic-converter",
    "arguments": {
  "operation": "power",
  "a": "17",
  "b": "5",
  "m": "13"
}
  }
}

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

Name

Type

Required

Description

operation

select

Yes

—

text

Yes

First operand (the base in power mode, the value being inverted in inverse mode).

text

Second operand — the exponent in power mode; unused in inverse mode.

text

Yes

Modulus, m ≥ 2. Results are reduced to the canonical range [0, m−1].

{ "mcpServers": { "elysiatools-modulo-arithmetic-converter": { "name": "modulo-arithmetic-converter", "description": "Exact BigInt modular arithmetic for values up to 10¹⁸: (a ± b) mod m, (a × b) mod m, a⁻¹ mod m via extended Euclid, and aᵇ mod m via fast exponentiation.", "baseUrl": "https://api.elysiatools.com/mcp/sse?toolId=modulo-arithmetic-converter", "command": "", "args": [], "env": {}, "isActive": true, "type": "sse" } } }

{ "jsonrpc": "2.0", "id": 2, "method": "tools/call", "params": { "name": "modulo-arithmetic-converter", "arguments": { "operation": "power", "a": "17", "b": "5", "m": "13" } } }