THE NUMBER OF RELATIVELY PRIME SUBSETS AND PHI FUNCTIONS FOR { m , m + 1 , . . . , n } Mohamed
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چکیده
The work in this paper is inspired and motivated by some work of Nathanson. We count the number of relatively prime subsets and the number of relatively prime subsets having some fixed cardinality that are in {m,m+1, . . . , n}. We also count the number of nonempty subsets of {m,m+1, . . . , n} whose gcd is relatively prime to n and the number of nonempty subsets {m,m+1, . . . , n} having some fixed cardinality and whose gcd is relatively prime to n. Our work generalizes the results on relatively prime subsets of {1, 2, . . . , n} and on phi functions for sets {1, 2, . . . , n}. Our proofs use an extension of the Möbius inversion formula to functions of several variables.
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تاریخ انتشار 2007