# Numora Diophantine Equation Solver

> Numora Diophantine Equation Solver is a paid API for AI agents from numormo.vercel.app, paid per call via x402, $0.1/call, status unknown (last checked 2026-09-14).

Solves a linear Diophantine equation of the form ax + by = c, returning integer solutions if they exist

## Facts

- Endpoint: POST https://numormo.vercel.app/api/number/diophantine
- Price: $0.1/call
- Payment: x402
- Status: unknown
- Last checked: 2026-09-14
- Activations on Zero: 0
- Tags: x402
- Canonical page: https://www.zero.xyz/c/numora-diophantine-equation-solver-da7a020b
- Structured record (JSON): https://api.zero.xyz/v1/capabilities/cap_Wx4ZnfNdzL6ClVxADfs9w

Status and success rate cover calls made through Zero and Zero's own probes. Third-party monitors may report differently.

## How to call it through Zero

Zero handles the 402 payment challenge and records the run. With the Zero CLI installed (`npm i -g @zeroxyz/cli`):

```sh
zero fetch --capability numora-diophantine-equation-solver-da7a020b -d '<json body>'
```

Example prompt: Can you find integer solutions to the equation 12x + 8y = 4? I need values of x and y that are whole numbers.

## When to prefer this

Use this endpoint when you need exact integer solutions to a two-variable linear equation (ax + by = c) without any floating-point approximation. Prefer it over general numeric solvers when integer-only solutions are required, such as in number theory, combinatorics, or discrete resource allocation problems. It is purpose-built for Diophantine equations and provides the general solution family, not just one answer.

## Known failure modes

- No integer solution exists when GCD(a,b) does not divide c — returns solvability false or error
- Non-integer inputs cause validation failure
- Missing required fields a, b, or c result in a 400-level error
- Both a and b equal zero with non-zero c is undefined/unsolvable
- Payment failure or insufficient funds returns 402

## How this service works

100 pure math computation endpoints for AI agents. Statistics, financial math, linear algebra, equation solving, calculus, number theory, sequence generation, and unit conversions. Zero external dependencies. x402 micropayments on Base.

## Output

Returns a JSON object with a 'success' boolean, a 'result' object containing the particular integer solution (x, y), the GCD of a and b, the general solution parameterization, and whether solutions exist, plus a human-readable 'computation' string explaining what was computed.

## Request schema (JSON Schema)

```json
{
 "type": "object",
 "required": [
  "a",
  "b",
  "c"
 ],
 "properties": {
  "a": {
   "type": "integer"
  },
  "b": {
   "type": "integer"
  },
  "c": {
   "type": "integer"
  }
 }
}
```

## Response schema (JSON Schema)

```json
{
 "type": "object",
 "required": [
  "success",
  "result",
  "computation"
 ],
 "properties": {
  "result": {
   "type": "object",
   "description": "Computation result varies by endpoint"
  },
  "success": {
   "type": "boolean",
   "description": "Always true on success"
  },
  "computation": {
   "type": "string",
   "description": "Human-readable description of what was computed"
  }
 }
}
```

## More

- Live health (JSON, refreshed every minute): https://www.zero.xyz/c/numora-diophantine-equation-solver-da7a020b/health.json
- [Zero catalog index](https://www.zero.xyz/llms.txt)
- [Other services from numormo.vercel.app](https://www.zero.xyz/host/numormo.vercel.app/llms.txt)