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math.LO2015★ 2 cited
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…
math.MG2015
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…