A simple proof of generalizations of number-theoretic sums
For positive integers 𝑘, 𝑚, and 𝑛, let 𝑆𝑘 𝑚(𝑛) be the sum of all elements in the finite set {𝑥 𝑘 : 1 ≤ 𝑥 ≤ 𝑛⁄𝑚 , (𝑥, 𝑛) = 1}. The formula for 𝑆𝑘 𝑚(𝑛) is established and simpler formulae for 𝑆𝑘 𝑚(𝑛) under some conditions on 𝑚 and 𝑛 are verified. The explicit formulae for 𝑆1 2 𝑎 (𝑛) and 𝑆2...
| Main Authors: | , |
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| Format: | Article |
| Language: | English |
| Published: |
Prince of Songkla University
2022-04-01
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| Series: | Songklanakarin Journal of Science and Technology (SJST) |
| Subjects: | |
| Online Access: | https://rdo.psu.ac.th/sjst/journal/44-2/22.pdf |