MathDB

C2

Part of 2010 Balkan MO Shortlist

Problems(1)

Grasshopper returns

Source: Balkan MO ShortList 2010 C2

4/5/2020
A grasshopper jumps on the plane from an integer point (point with integer coordinates) to another integer point according to the following rules: His first jump is of length 98\sqrt{98}, his second jump is of length 149\sqrt{149}, his next jump is of length 98\sqrt{98}, and so on, alternatively. What is the least possible odd number of moves in which the grasshopper could return to his starting point?