# Numora Diophantine Equation Solver

> Numora Diophantine Equation Solver is a paid API for AI agents from numorapoi.orbonomy.xyz, paid per call via x402, $0.03/call, status unknown (last checked 2026-10-15).

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

## Facts

- Endpoint: POST https://numorapoi.orbonomy.xyz/api/number/diophantine?utm_source=zero.xyz
- Price: $0.03/call
- Payment: x402
- Status: unknown
- Last checked: 2026-10-15
- Activations on Zero: 0
- Tags: x402
- Canonical page: https://www.zero.xyz/c/numora-diophantine-equation-solver-0fe1738f
- Structured record (JSON): https://api.zero.xyz/v1/capabilities/cap_sEQhqYcns5AAvaN_6kXtp

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-0fe1738f -d '<json body>'
```

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

## When to prefer this

Use this endpoint when you need to determine whether integers x and y exist satisfying ax + by = c, or when you need a particular integer solution to such an equation. Prefer this over general algebra solvers when you specifically need integer (not real-valued) solutions and want a pure-math, dependency-free computation with micropayment pricing per call.

## Known failure modes

- No integer solution exists when gcd(a,b) does not divide c — endpoint should return success:false or a result indicating no solution
- Missing required fields a, b, or c return a validation error
- Non-integer inputs for a, b, c cause schema validation failure
- Payment failure via x402 if USDC balance is insufficient
- Server error if coefficients are extremely large causing overflow

## 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 boolean success flag, a result object containing integer solutions (x, y) if they exist or a message indicating no solution exists, and a human-readable computation string describing what was solved.

## 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-0fe1738f/health.json
- [Zero catalog index](https://www.zero.xyz/llms.txt)
- [Other services from numorapoi.orbonomy.xyz](https://www.zero.xyz/host/numorapoi.orbonomy.xyz/llms.txt)