MathDB

1

Part of 2015 Azerbaijan IMO TST

Problems(2)

2015 Azerbaijan IMO TST

Source: 2015 Azerbaijan IMO TST

5/29/2015
We say that AA=={a1,a2,a3⋯ana_1,a_2,a_3\cdots a_n} consisting n>2n>2 distinct positive integers is goodgood if for every i=1,2,3⋯ni=1,2,3\cdots n the number ai2015{a_i}^{2015} is divisible by the product of all numbers in AA except aia_i. Find all integers n>2n>2 such that exists a goodgood set consisting of nn positive integers.
Combinatorial Number Theorycombinatorics
Azerbaijan IMO TST

Source:

9/15/2015
Let ω\omega be the circumcircle of an acute-angled triangle ABCABC. The lines tangent to ω\omega at the points AA and BB meet at KK. The line passing through KK and parallel to BCBC intersects the side ACAC at SS. Prove that BS=CSBS=CS
geometrycircumcircle