MathDB

1

Part of 2010 Thailand Mathematical Olympiad

Problems(2)

no of ways to distribute 11 balls into 5 boxes with different sizes

Source: 2010 Thailand Mathematical Olympiad day 1 p1

3/12/2021
Find the number of ways to distribute 1111 balls into 55 boxes with different sizes, so that each box receives at least one ball, and the total number of balls in the largest and smallest boxes is more than the total number of balls in the remaining boxes.
combinatorics
for every x exists y in {2, 5, 13} such that xy - 1 not a perfect square

Source: Thailand Mathematical Olympiad 2010 day 2 p1

8/17/2020
Show that, for every positive integer xx, there is a positive integer y∈{2,5,13}y\in \{2, 5, 13\} such that xy−1xy - 1 is not a perfect square.
number theoryPerfect Square