8 citations · 13 across the 7 of their papers we have counts for
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Generalized Schatunowsky theorem in a weak arithmetic
Hala King, Victor Pambuccian
Schatunowsky's 1893 theorem, that 30 is the largest number all of whose totatives are primes, has been recently generalized by Kaneko and Nakai. In its generalized form, it states…
A problem in Pythagorean Arithmetic
Victor Pambuccian
Problem 2 at the 56th International Mathematical Olympiad (2015) asks for all triples (a,b,c) of positive integers for which ab-c, bc-a, and ca-b are all powers of 2. We show that…
An axiomatic look at a windmill
Victor Pambuccian
We present the problem stated in intuitive language as problem 2 at the 52nd International Mathematical Olympiad as a formal statement, and prove that it is valid in ordered regula…
The sum of irreducible fractions with consecutive denominators is never an integer in a very weak arithmetic
Victor Pambuccian
Two theorems of elmentary arithmetic, one stating that the sum of the reciprocals of any number of consecutive positive integers is never an integer, and a generalization thereof b…