🔺 生成整数三元组（勾股等）Generate Integer Triples
生成整数三元组：勾股数（a^2+b^2=c^2）、连续三整数，或和为 S 的随机三元组（可设种子）。本地处理。Generate integer triples: Pythagorean triples, three consecutive integers, or random triples that sum to S (optional seed). Processed locally.
使用说明与常见问题How-to & FAQ
「生成整数三元组（勾股等）」是什么？What is the Generate Integer Triples tool?
生成整数三元组：勾股数（a^2+b^2=c^2）、连续三整数，或和为 S 的随机三元组（可设种子）。本地处理。Generate integer triples: Pythagorean triples, three consecutive integers, or random triples that sum to S (optional seed). Processed locally.
如何使用「生成整数三元组（勾股等）」？How do I use the Generate Integer Triples tool?
在「生成整数三元组（勾股等）」中，按需设置「类型」、「组数」、「连续起始」、「目标和 S」、「种子」，结果会实时显示在下方，点击「复制结果」即可复制。Choose the "Kind" of triple (Pythagorean, three consecutive integers, or random triples that add up to S) and "How many" to list; "Consecutive start", "Target sum S" and "Seed" apply to the matching kind. The list updates as you change a setting; click "Copy result" to copy it.
勾股数怎样生成？How are Pythagorean triples made?
用经典公式：对整数 u>v>0 且一奇一偶，a=|u^2-v^2|, b=2uv, c=u^2+v^2。The classic formula: for integers u>v>0 of opposite parity, a=|u^2-v^2|, b=2uv, c=u^2+v^2.
连续三整数和和为 S 支持哪些数？Which values work for Consecutive and Sum to S?
「连续起始」和「目标和 S」可以是 0、负数或任意大的整数（按大整数计算，9007199254740993 也精确）；小数会提示错误。种子只影响「和为 S 的随机」；这个工具不需要输入框，所以页面上没有输入区。Consecutive start and Target sum S can be 0, negative or arbitrarily large (big-integer arithmetic, so 9007199254740993 stays exact); decimals give an error. The seed only affects Random sum to S; this tool has no text input, so the input box is hidden.
输入和输出是什么样的？What does the input and output look like?
例如在「生成整数三元组（勾股等）」中把「类型」设为 勾股数，「组数」设为 2，输出为：3 4 5 ⏎ 5 12 13（⏎ 表示换行）。For example, in the Generate Integer Triples with "Kind" set to Pythagorean, "How many" set to 2, the output is: 3 4 5 ⏎ 5 12 13 (⏎ marks a line break).
有哪些选项可以调整？What options can I adjust?
「生成整数三元组（勾股等）」的设置：「类型」可选 勾股数、连续三整数、和为 S 的随机（默认 勾股数）；「组数」默认 5；「连续起始」默认 1；「目标和 S」默认 10；「种子」可留空。改动任一选项后结果会按新设置重新生成。Settings in the Generate Integer Triples — "Kind": Pythagorean, Consecutive, Random sum to S (default Pythagorean); "How many" default 5; "Consecutive start" default 1; "Target sum S" default 10; "Seed" optional. Changing any option regenerates the result with the new setting.
「生成整数三元组（勾股等）」免费吗？需要注册吗？Is the Generate Integer Triples free? Do I need an account?
「生成整数三元组（勾股等）」完全免费，无需注册或安装，打开网页即可使用，手机和电脑都能用；输入的内容只在你的浏览器本地处理。The Generate Integer Triples is completely free with no sign-up or install and works on phones and desktops; what you enter is processed only in your browser.