2016 JBMO Problems
A trapezoid (,) is circumscribed.The incircle of the triangle touches the lines and at the points and ,respectively.Prove that the incenter of the trapezoid lies on the line .
Let be positive real numbers.Prove that
Find all triplets of integers such that the number
is a power of .
(A power of is an integer of form ,where is a non-negative integer.)
A table is called regular f each of its cells contains one of four pairwise distinct real numbers,such that each of them occurs exactly one in every subtable.The sum of all numbers of a regular table is called the total sum of the table.With any four numbers,one constructs all possible regular tables,computes their total sums and counts the distinct outcomes.Determine the maximum possible count.
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