Extends totient generalizations from Toth 2022 using elementary symmetric sums, derives product forms for the second sum, and demonstrates equivalences to finite-field zero counting and restricted linear congruences.
E1460.The American Mathe- matical Monthly, 68(9):932–933
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Some Generalizations of Totient Function with Elementary Symmetric Sums
Extends totient generalizations from Toth 2022 using elementary symmetric sums, derives product forms for the second sum, and demonstrates equivalences to finite-field zero counting and restricted linear congruences.