ForHosting KIT · Developer Utilities

Chinese remainder theorem solver

The Chinese remainder theorem solver takes a system of simultaneous congruences — x congruent to each remainder a_i modulo each modulus n_i — and returns the unique solution class when one exists.

● BetaFree · in your browser

Run — free How it works & API

Use it from WebAPIEmailTelegramApp soon

You supply parallel arrays of remainders and moduli; the engine folds them with successive CRT, checks consistency when moduli share factors, and reports both the representative x in zero through modulus minus one and the modulus of the solution class (the product of the n_i when they are pairwise coprime, otherwise their least common multiple). The path is pure integer arithmetic: no network, no randomness, and no clock. Use it free in the browser for homework, contest practice, and modular-arithmetic demos, or call the API at $0.002 per successful request when grading scripts, crypto teaching tools, or CI fixtures need reproducible CRT answers.

How to use it

Enter your values in the form above. The tool checks them before calculating and shows the result on the same page.

Check your inputs

Use the labels and units shown next to each field. If something is missing or outside the allowed range, the page points to the field to fix.

Use it again or automate it

Use the browser tool for individual checks and the API when you need the same capability in an automated workflow.

What you can do with it

Get an answer now

Enter one set of values and see the result without building a spreadsheet or script.

Compare scenarios

Change one value at a time and rerun the calculation to understand what affects the result.

Automate repeated work

Use the API when the same calculation needs to run inside your product or workflow.

FAQ

How do I use this capability?

Complete the fields above and run it on this page. The form highlights anything that needs attention.

For developers — API access

Everything on this page is available programmatically. This section is for teams who want to wire it into their own systems; everyone else can just use the tool above.

API endpoint

POSThttps://api.kit.forhosting.com/numth/chinese-remainder

Prefer to automate it? One authenticated POST creates the task; the result comes back by webhook or a signed link. The same capability also runs here on the web, by email and from Telegram — and soon from our app too.

Call it from your stack

curl -X POST https://api.kit.forhosting.com/numth/chinese-remainder \
  -H "Authorization: Bearer $KIT_KEY" \
  -H "Content-Type: application/json" \
  -d '{"remainders":[2,3,2],"moduli":[3,5,7]}'

const res = await fetch("https://api.kit.forhosting.com/numth/chinese-remainder", {
  method: "POST",
  headers: {
    "Authorization": `Bearer ${process.env.KIT_KEY}`,
    "Content-Type": "application/json"
  },
  body: JSON.stringify({
    "remainders": [
      2,
      3,
      2
    ],
    "moduli": [
      3,
      5,
      7
    ]
  })
});
const { task_id } = await res.json();

import os, requests

res = requests.post(
    "https://api.kit.forhosting.com/numth/chinese-remainder",
    headers={"Authorization": f"Bearer {os.environ['KIT_KEY']}"},
    json={
    "remainders": [
        2,
        3,
        2
    ],
    "moduli": [
        3,
        5,
        7
    ]
},
)
task_id = res.json()["task_id"]

<?php
$res = file_get_contents("https://api.kit.forhosting.com/numth/chinese-remainder", false, stream_context_create([
  "http" => [
    "method"  => "POST",
    "header"  => "Authorization: Bearer " . getenv("KIT_KEY") . "\r\nContent-Type: application/json",
    "content" => '{"remainders":[2,3,2],"moduli":[3,5,7]}',
  ],
]));
$task = json_decode($res, true);

body := bytes.NewBufferString(`{"remainders":[2,3,2],"moduli":[3,5,7]}`)
req, _ := http.NewRequest("POST", "https://api.kit.forhosting.com/numth/chinese-remainder", body)
req.Header.Set("Authorization", "Bearer "+os.Getenv("KIT_KEY"))
req.Header.Set("Content-Type", "application/json")
res, _ := http.DefaultClient.Do(req)

Example request

{
  "remainders": [
    2,
    3,
    2
  ],
  "moduli": [
    3,
    5,
    7
  ]
}

Example response

{
  "task_id": "tsk_a1b2c3d4e5f6a1b2c3d4e5f6",
  "type": "numth.chinese_remainder",
  "status": "queued",
  "_links": {
    "result": "/tasks/tsk_…/result"
  }
}

The API is asynchronous: the call returns a task_id immediately and the result arrives by webhook. Polling is capped at 1 req/s per task.

Pricing

Per request$0.002

Published price — no tokens, no invented credits. A failed task is never charged.

Errors

HTTP	Code	Meaning
`401`	`unauthorized`	Missing or invalid API key.
`402`	`insufficient_balance`	Your balance doesn't cover the task price.
`404`	`unknown_type`	That task type doesn't exist.
`429`	`rate_limited`	Too many requests. Use the webhook instead of polling.

Read the full KIT documentation →

Run — free