Math & Numbers
Jacobi/Legendre symbol with deterministic Miller–Rabin primality, Tonelli–Shanks square roots for prime moduli, and brute-force resolution for small composite moduli.
Call this tool from your code in three languages.
curl -X POST 'http://127.0.0.1:3003/en/api/tools/quadratic-residue-checker' \
-H 'Content-Type: application/json' \
-d '{"a":"10","n":"13","solveRoots":true}'Send a POST request with your inputs as JSON. File parameters require a separate upload first.
POST http://127.0.0.1:3003/en/api/tools/quadratic-residue-checker| Name | Type | Required | Description |
|---|---|---|---|
| a | text | Yes | The value being tested for squareness; reduced mod n first (up to 10⁵¹²). |
| n | text | Yes | Odd modulus, 3 ≤ n ≤ 10¹⁸ (primality tested with deterministic Miller–Rabin). |
| solveRoots | checkbox | No | Run Tonelli–Shanks and print the square roots when they exist. |
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-quadratic-residue-checker": {
"name": "quadratic-residue-checker",
"description": "Jacobi/Legendre symbol with deterministic Miller–Rabin primality, Tonelli–Shanks square roots for prime moduli, and brute-force resolution for small composite moduli.",
"baseUrl": "http://127.0.0.1:3003/mcp/sse?toolId=quadratic-residue-checker",
"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": "quadratic-residue-checker",
"arguments": {
"a": "10",
"n": "13",
"solveRoots": true
}
}
}Questions or issues? Contact [email protected]