MathDB

A one-person game with two possible outcomes is played as follows: After each play, the player receives either

a

b

points, where

a

and

b

are integers with

0 < b < a < 1986

. The game is played as many times as one wishes and the total score of the game is defined as the sum of points received after successive plays. It is observed that every integer

x \geq 1986

can be obtained as the total score whereas

1985

and

663

cannot. Determine

a

and

b.

Problem Statement