# Numora Diophantine Equation Solver

> Numora Diophantine Equation Solver is a paid API for AI agents from numomo.vercel.app, paid per call via x402, $0.1/call, status unknown (last checked 2026-09-15).

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

## Facts

- Endpoint: POST https://numomo.vercel.app/api/number/diophantine
- Price: $0.1/call
- Payment: x402
- Status: unknown
- Last checked: 2026-09-15
- Activations on Zero: 0
- Tags: x402
- Canonical page: https://www.zero.xyz/c/numora-diophantine-equation-solver-31f8bd03
- Structured record (JSON): https://api.zero.xyz/v1/capabilities/cap_XZcufIkO5Qne46uRK64ef

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-31f8bd03 -d '<json body>'
```

Example prompt: Can you solve the Diophantine equation 3x + 7y = 1 and find integer values of x and y that satisfy it?

## When to prefer this

Choose this endpoint when you need to solve a two-variable linear equation strictly over the integers (Diophantine form ax + by = c), particularly in number theory, cryptography (Bezout coefficients), modular arithmetic, or combinatorial resource allocation problems. Prefer over general equation solvers when integer constraints are mandatory and you need the complete parametric family of solutions.

## Known failure modes

- Both a and b are zero (undefined equation, no unique solution)
- c is not divisible by gcd(a, b) meaning no integer solution exists — endpoint returns success:true but indicates unsolvable
- Non-integer inputs rejected with 400 error
- Missing required fields a, b, or c return validation error
- Payment not included or insufficient triggers x402 payment required response

## 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 success flag, a human-readable description of the computation, and a result object containing whether integer solutions exist, a particular solution (x0, y0) if solvable, the GCD of a and b, and the general solution parametric form (e.g. x = x0 + (b/gcd)t, y = y0 - (a/gcd)t for any integer t).

## 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-31f8bd03/health.json
- [Zero catalog index](https://www.zero.xyz/llms.txt)
- [Other services from numomo.vercel.app](https://www.zero.xyz/host/numomo.vercel.app/llms.txt)