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math.NT2013
A Theorem involving the denominators of Bernoulli numbers
Pantelis A. Damianou, Peter Schumer
Consider the average of the first n k-th powers. We pose and answer the following natural question: For which values of n and k is this average an integer? If k is odd the answer i…
math-ph2013
On generalized Volterra systems
Stelios A. Charalambides, Pantelis A. Damianou, Charalampos A. Evripidou
We construct a large family of evidently integrable Hamiltonian systems which are generalizations of the KM system. The Hamiltonian vector field is homogeneous cubic but in a numbe…