Math & Numbers

Multiplicative Order Calculator mod n (ordₙ(a))

Smallest k with a^k ≡ 1 (mod n) via φ(n) reduction: power table, minimality proof, cyclic subgroup <a>, primitive-root and maximal-order flags.

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/order-of-element-mod-n' \
  -H 'Content-Type: application/json' \
  -d '{"a":"3","n":"7"}'

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/order-of-element-mod-n

Parameters

Name	Type	Required	Description
a	text	Yes	The element whose order is computed; reduced mod n first (up to 10⁵¹²).
n	text	Yes	Modulus, 2 ≤ n ≤ 10¹² (needs factorization of n and φ(n)).

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-order-of-element-mod-n": {
      "name": "order-of-element-mod-n",
      "description": "Smallest k with a^k ≡ 1 (mod n) via φ(n) reduction: power table, minimality proof, cyclic subgroup <a>, primitive-root and maximal-order flags.",
      "baseUrl": "https://api.elysiatools.com/mcp/sse?toolId=order-of-element-mod-n",
      "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": "order-of-element-mod-n",
    "arguments": {
  "a": "3",
  "n": "7"
}
  }
}

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

text

Yes

The element whose order is computed; reduced mod n first (up to 10⁵¹²).

text

Yes

Modulus, 2 ≤ n ≤ 10¹² (needs factorization of n and φ(n)).

{ "mcpServers": { "elysiatools-order-of-element-mod-n": { "name": "order-of-element-mod-n", "description": "Smallest k with a^k ≡ 1 (mod n) via φ(n) reduction: power table, minimality proof, cyclic subgroup <a>, primitive-root and maximal-order flags.", "baseUrl": "https://api.elysiatools.com/mcp/sse?toolId=order-of-element-mod-n", "command": "", "args": [], "env": {}, "isActive": true, "type": "sse" } } }