let bi = (here we define a0 to be an and an+1 to be a1).

Sunday, April 16, 2023 Problem 4. Turbo the snail sits on a point on a circle with circumference 1. Given an in nite sequence of positive real numbersc 1;c 2;c 3;:::, Turbo successively crawls …

Saturday, April 15, 2023 Problem 1. There aren > 3 positive real numbers a 1;a 2;:::;a n. For each1 6 i 6 n we let b

SĹbbato, 15 AprilÐou, 2023 Prìblhma 1. ’Estw n > 3 jetikoÐ pragmatikoÐ arijmoÐ a 1;a 2;:::;a n. Gia kĹje 1 6 i 6 n jètoume b

2023 M 4 15 ° - Û B 5 " RX óç n > 3 n ñ L a1;a2; ;anX Äñ i = 1 ;2; ;n - : bi= ai 1+ ai+1 ai U Ú - á Ì ÿç a0= an- an +1= a1VX L ! î µ i;j 2 f 1;2; ;n g- û µ ai6 aj OÇ bi6 bjX £ ü , a1= a2= = anX 5 " kX !

4-ð ñàðûí 15-íû Áßìáà ãàðàã, 2023 îí Áîäëîãî 1. a 1;a 2;:::;a nãýñýí n > 3 øèðõýã ýåðýã áîäèò òîîíóóä řãřãäřâ. 1 6 i 6 n áàéõ i äóãààð áşðèéí õóâüä b

Sábado, 15 de abril de 2023 Problema 1. Se tienenn >3 números reales positivosa 1;a 2;:::;a n. Para cada16 i 6 n se de ne b