TY - JOUR AU - Narakorn Rompurk Kanasri, AU - Arlisa Janjing, PY - 2022/12/31 Y2 - 2024/03/29 TI - Some Number-Theoretic Products JF - Science & Technology Asia JA - Sci Tech Asia VL - 27 IS - 4 SE - DO - UR - https://ph02.tci-thaijo.org/index.php/SciTechAsia/article/view/247953 SP - 228-235 AB - <p>For a positive integer <em>n</em>, let <em>P</em>(<em>n</em>) and <em>P</em>′&nbsp;(<em>n</em>) be the products of all elements in the finite sets {<em>x</em>: 1 ≤ <em>x</em> ≤ <em>n</em>, (<em>x, n</em>) = 1} and {<em>x</em> : 1 ≤ <em>x</em> ≤ <em>n/</em>2, (<em>x, n</em>) = 1}, respectively. In this article, we verify the formula for <em>P</em>(<em>n</em>) and use it to establish the formula for <em>P</em>′ (<em>n</em>). Explicit formulae for both <em>P</em> (<em>pa</em>) and <em>P</em>′ (<em>pa</em>), where <em>pa</em> is a prime power, are also derived.</p> ER -