lucas_theorem
Compute binomial coefficient C(n,k) mod prime using Lucas' theorem.
This record as markdown: /tools/io-github-malamutemayhem-unclick-mcp-server/lucas-theorem.md
What lucas_theorem does on UnClick
AI agents call lucas_theorem to retrieve information from UnClick without modifying anything. It is typically the context-gathering step in research, monitoring, and reporting workflows, before the agent takes action elsewhere.
| Parameter | Type | Required | Description |
|---|---|---|---|
k | number | Yes | Non-negative integer k (k <= n) |
n | number | Yes | Non-negative integer n |
p | number | Yes | Prime modulus |
Parameters from the server's own tool schema.
Why lucas_theorem is rated Low
This is a mathematical utility function that retrieves a calculated result (binomial coefficient modulo a prime). It performs no data creation, modification, deletion, code execution, or financial operations. The computation is deterministic and side-effect free, making it a Read operation with minimal risk.
From the tool's definition Tool computes and returns a binomial coefficient using Lucas' theorem; no modification, deletion, or execution of external operations occurs. Pure mathematical computation with no side effects.
Attacks that exploit this kind of access
The rule that runs lucas_theorem safely
PolicyLayer is an MCP gateway: it sits between your AI agents and UnClick, and checks every tool call against a rule you set before the call runs. Nothing changes on the server itself. For lucas_theorem, this is the rule to start with:
lucas_theorem is read-only, so it stays allowed. Everything else on the server is denied unless you say otherwise.
The button opens the PolicyLayer dashboard: create your workspace, connect UnClick, apply this rule, and every lucas_theorem call is checked against it from then on.
Questions about lucas_theorem
Compute binomial coefficient C(n,k) mod prime using Lucas' theorem. It is categorised as a Read tool in the UnClick MCP Server, which means it retrieves data without modifying state.
lucas_theorem accepts 3 parameters: k, n, p. Required: k, n, p. The full parameter table on this page comes from the server's own tool schema.
Register the UnClick MCP server in PolicyLayer and add a rule for lucas_theorem: allow, deny, rate-limit, or require approval. Point your MCP client at the PolicyLayer proxy URL and the rule is enforced on every call, before it reaches UnClick. Nothing to install.
lucas_theorem is a Read tool with low risk. Read-only tools are generally safe to allow by default.
Yes. Add a rate_limit block to the lucas_theorem rule in your PolicyLayer policy. For example, setting max: 10 and window: 60 limits the tool to 10 calls per minute. Rate limits are tracked per agent session and reset automatically.
Set action: deny in the PolicyLayer policy for lucas_theorem. The AI agent will receive a policy violation error and cannot call the tool. You can also include a reason field to explain why the tool is blocked.
lucas_theorem is provided by the UnClick MCP server (@unclick/mcp-server). PolicyLayer sits as a proxy in front of this server to enforce policies before tool calls reach the server.
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