# Numora Diophantine Equation Solver

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

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

## Facts

- Endpoint: POST https://numormor.netlify.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-72db1600
- Structured record (JSON): https://api.zero.xyz/v1/capabilities/cap_38UnDdlqsx-UbZbKa6i1Q

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-72db1600 -d '<json body>'
```

Example prompt: Can you solve the Diophantine equation where a=17, b=13, and c=1 — I need integer values of x and y that satisfy 17x + 13y = 1?

## When to prefer this

Use this endpoint when you need exact integer solutions to a linear two-variable equation of the form ax + by = c — a classic number theory problem. Prefer this over general equation solvers when you specifically need integer (not real) solutions, or when applying the extended Euclidean algorithm. Ideal for cryptographic key problems, modular inverse computations, and combinatorial integer constraints.

## Known failure modes

- No solution exists when gcd(a,b) does not divide c — result may indicate unsolvability
- Payment failure or 402 response if x402 micropayment is not properly configured
- Invalid input types if a, b, or c are not integers — schema validation error
- Edge case: a=0 and b=0 with c≠0 is unsolvable; a=0 and b=0 with c=0 is trivially infinite solutions

## 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 success=true, a result object containing the particular integer solution (x, y) if one exists (or a flag indicating no solution exists when gcd(a,b) does not divide c), and a human-readable computation string describing what was solved and how.

## 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-72db1600/health.json
- [Zero catalog index](https://www.zero.xyz/llms.txt)
- [Other services from numormor.netlify.app](https://www.zero.xyz/host/numormor.netlify.app/llms.txt)