MathDB

4

Part of 2016 Israel Team Selection Test

Problems(2)

Subsets of vertices with no isosceles triangles

Source: Israel Autumn 2016 TST1/4

9/29/2016
A regular 60-gon is given. What is the maximum size of a subset of its vertices containing no isosceles triangles?
combinatoricscombinatorics solved
Greates Common Divisor of a Set

Source: Israel Autumn 2016 TST2/4

9/29/2016
Find the greatest common divisor of all numbers of the form (2a2⋅19b2⋅53c2+8)16−1(2^{a^2}\cdot 19^{b^2} \cdot 53^{c^2} + 8)^{16} - 1 where a,b,ca,b,c are integers.
greatest common divisornumber theorynumber theory solved