MathDB

Bosnia and Herzegovina TST 1996 Day 2 Problem 3

Source: Bosnia and Herzegovina Team Selection Test 1996

September 20, 2018

probabilitynumber theoryfloor function

Problem Statement

Let

a

and

b

be two integers which are coprime and let

n

be one variable integer. Determine probability that number of solutions

(x,y)

, where

x

and

y

are nonnegative integers, of equation

ax+by=n

\left\lfloor \frac{n}{ab} \right\rfloor + 1