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Crypto Math: Chinese Remainder Theorem Solver
x402
Crypto Math: Chinese Remainder Theorem Solver is a paid API for AI agents from crypto-math.x402tookit.com, paid per call via x402, $0.02/call, status unknown (last checked 2026-10-29).
Solves systems of simultaneous congruences (x ≡ a1 mod m1, x ≡ a2 mod m2, …) using the Chinese Remainder Theorem, supporting both coprime and non-coprime moduli.
Price / call$0.02
Success—
StatusUnknown
How this service works
Solve x = a1 (mod m1), x = a2 (mod m2), ... with the Chinese remainder theorem, coprime or not.
Output
Returns the solution x (smallest non-negative integer satisfying all congruences), the combined modulus, a human-readable equation string, a summary of the computation, a verdict on whether a solution exists, and optional reasons if no solution is found. Also includes a degraded flag and disclaimer if relevant.
Example use cases
Cryptographic key reconstruction
“I need to recover a value using the Chinese Remainder Theorem from these congruences: 6:11, 9:13, 17:19 — what is x and the combined modulus?”
Number theory homework check
“Can you solve this system of congruences for me: x ≡ 2 mod 3, x ≡ 3 mod 5, x ≡ 2 mod 7? Use the CRT and tell me if a solution exists and what it is.”
Non-coprime moduli feasibility check
“I have these congruences: 4:6, 3:9 — are the moduli non-coprime, and does a solution still exist? Run the CRT and show me the result or why it fails.”
Technical details
Endpoint
GEThttps://crypto-math.x402tookit.com/crt?utm_source=zero.xyzWhen to prefer
Choose this endpoint when you need to solve a system of simultaneous modular congruences — especially when moduli may not be pairwise coprime and a generalized CRT is required. Ideal for cryptographic computations (e.g. RSA CRT optimization), number theory problems, and scheduling or calendar calculations based on modular cycles. Prefer over general-purpose CAS tools when you need a lightweight, paid-per-call API with structured output including solvability verdict and modulus.
Side effects
- No solution exists when moduli are non-coprime and residues are incompatible — returns null x with reasons
- Malformed congruences string (wrong separator, non-integer values) causes a 400-style error
- Fewer than 2 or more than 12 congruence pairs may be rejected
- Overflow or extremely large integers may cause computation failure
- Missing required 'congruences' query parameter returns an error
Input
Schema · Request body
| Field | Type | Description |
|---|---|---|
| inputrequired | object | |
| output | object |
Tags
x402
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