IMO 2020 Problem 5
- Day 2
A deck of cards is given. A positive integer is written on each card. The deck has the property that the arithmetic mean of the numbers on each pair of cards is also the geometric mean of the numbers on some collection of one or more cards. For which does it follow that the numbers on the cards are all equal?
Proposed by Oleg Košik, Estonia
Official text Transcription from AI-MO AoPS, checked word for word against the official paper. Quoted with source.
Official text: IMO 2020 official English paper, page 2.
Solutions
No solution is on olymmath yet. Official and human solutions come first when they arrive. AI solutions come after them, with a label.