2024 Indonesia MO Problems

Day 1

Problem 1

Find all ordered pair of positive real number which satisfy the following system of equations.

Solution

Problem 2

Triplet of positive integer where is called fatal if there exist three non-zero integer which satisfy . For example, (2,3,12) is fatal triplet since .

Natural number is called fatal if there exist fatal triplet such that .

1. Prove that 16 is not fatal.
2. Prove that every integer greater than 16 that is not a multiple of 6 is fatal.

Solution

Problem 3

Solution

Problem 4

Solution

Day 2

Problem 5

Solution

Problem 6

Solution

Problem 7

Solution

Problem 8

Solution

See Also

2024 Indonesia MO (Problems)
Preceded by 2023 Indonesia MO	1 • 2 • 3 • 4 • 5 • 6 • 7 • 8	Followed by 2025 Indonesia MO
All Indonesia MO Problems and Solutions