MathDB

A2

Part of 2016 Costa Rica - Final Round

Problems(2)

diophantine p (x + y) = xy OLCOMA Costa Rica Final 2016 Shortlist A2 D1

Source:

9/23/2021
Find all integer solutions of the equation p(x+y)=xyp (x + y) = xy, where pp is a prime number.
number theorydiophantineDiophantine equation
perfect square +1000= other perfect square +1

Source: OLCOMA Costa Rica National Olympiad, Final Round, 2016 Shortlist A2 day2

9/24/2021
The initial number of inhabitants of a city of more than 150150 inhabitants is a perfect square. With an increase of 10001000 inhabitants it becomes a perfect square plus a unit. After from another increase of 10001000 inhabitants it is again a perfect square. Determine the quantity of inhabitants that are initially in the city.
number theoryPerfect SquaresPerfect Square