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  "aliases": [
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  "body": "\n## Summary\n\nIn mathematics, **Bhargava's factorial function**, or simply the **Bhargava factorial**, is a generalization of the [[factorial|0XWG0JGDFW]] function developed by Manjul Bhargava as part of his bachelor's thesis at Harvard University in 1996. Bhargava subsequently published a revised version in *The American Mathematical Monthly* in 2000. The Bhargava factorial has the property that many number-theoretic results involving the ordinary factorials remain true even when the factorials are replaced by the Bhargava factorials. Using an arbitrary [[infinite subset|01MKW4R283]] *S* of the set $\\mathbb{Z}$ of integers, Bhargava associated a positive integer with every positive integer *k*, which he denoted by *k* !\u003csub\u003e*S*\u003c/sub\u003e, with the property that if one takes *S* = $\\mathbb{Z}$ itself, then the integer associated with *k*, that is *k* !\u003csub\u003e$\\mathbb{Z}$\u003c/sub\u003e, would turn out to be the ordinary factorial of *k*.\n",
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