8 citations · 13 across the 7 of their papers we have counts for
8 papers
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…
The Steiner-Lehmus theorem and "triangles with congruent medians are isosceles" hold in weak geometries
Victor Pambuccian, Horst Struve, Rolf Struve
We prove that (i) a generalization of the Steiner-Lehmus theorem due to A. Henderson holds in Bachmann's standard ordered metric planes, (ii) that a variant of Steiner-Lehmus holds…
The Erdős-Selfridge and the Schinzel-Tijdeman theorems hold in
Victor Pambuccian
We show that "The product of consecutive integers is never a power" and several results by Schinzel and Tijdeman on the solutions of the equation , for , , and…
On the axiomatics of projective and affine geometry in terms of line intersection
Hans Havlicek, Victor Pambuccian
By providing explicit definitions, we show that in both affine and projective geometry of dimension , considered as first-order theories axiomatized in terms of lines as th…
A definitional view of Vogt's variant of the Mazur-Ulam theorem
Victor Pambuccian
A rephrasing of Vogt's and Skof's version of the Ulam-Mazur theorem as a definability statement.
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…