Math & Numbers
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.
Call this tool from your code in three languages.
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"}'Send a POST request with your inputs as JSON. File parameters require a separate upload first.
POST https://api.elysiatools.com/en/api/tools/order-of-element-mod-n| 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)). |
Text result
{
"result": "Processed text content",
"error": "Error message (optional)",
"message": "Notification message (optional)",
"metadata": {
"key": "value"
}
}Add this tool to your Model Context Protocol server so AI agents can list and call it.
Add this block to your MCP client configuration:
{
"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"
}
}
}After connecting to the SSE endpoint, list the exposed tools:
{
"jsonrpc": "2.0",
"id": 1,
"method": "tools/list"
}Invoke the tool by its id, passing arguments built from its parameters:
{
"jsonrpc": "2.0",
"id": 2,
"method": "tools/call",
"params": {
"name": "order-of-element-mod-n",
"arguments": {
"a": "3",
"n": "7"
}
}
}Questions or issues? Contact [email protected]