Bagi yang sudah kelaperan pingin ngerjain soal. Ini aku kasih problem dari Olimpiade matematika Yunani 2010. Soal aku terjemahkan sesuai pemahamanku.
Problem 1. Carilah solusi integer dari persamaan Diophantine berikut :
Problem 2. Jika
Kapan kesamaan terjadi?
Sory yang problem 3 dan 4 tidak aku terjemahkan, aku kasih apa adanya dalam bahasa inggris. Takut nerjemahkannya salah karena aku tidak suka ma geometry ( sama sekali gelap ). Klo yang 4 sih combin tapi pake unsur di geometry jadinya gelap lagi.
Problem 3. A triangle is inscribed in a circle
and has incenter
. Lines
meet the circumcircle
of triangle
at points
respectively. The circles with diameter
meet the sides
at pairs of points
respectively. Prove that the six points
are concyclic.
Problem 4. On the plane are given distinct lines, where
is integer and
is integer as well. Any three of these lines do not pass through the same point . Among these lines exactly
are parallel and all the other
lines intersect each other. All
lines define on the plane a partition of triangular , polygonic or not bounded regions. Two regions are colled different, if the have not common points or if they have common points only on their boundary. A regions is called ''good'' if it contained in a zone between two parallel lines . If in a such given configuration the minimum number of ''good'' region is 176 and the maximum number of these regions is 221 , find
and
.

Please, give me solution or hit for number 3 and 4. Thanks.
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