Academic Seminar (Course)
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SEMINAR:On the sum of the k-th powers of positive integers that are...
in LaTeX format) For given positive integers n and k, the sum of the k-th powers of the first n consecutive integers can be given as
S_k(n)1k+cdots +nksum_m1nmk.
Similarly, we define the sum of the k-th powers of the first varphi(n) positive integers that are coprime to n as
varphi_k(n) sum_substacka1 (a,n)1n ak,
where varphi(n) denotes the Euler-phi function. It is well-known that for all n 0 the sum S_1(n) divides S_k(n) when k is odd. Motivated by this result, in this talk we deal with the positive integer values of k for which the sum varphi_1(n) divides varphi_k(n) for all n 0. More generally, we define the set
06.05.2024 - All Day