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math.LO2025
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…
math.LO2012
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…
math.LO2008
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…