MathDB

RMO 2016 ,Q3

Source: Oct 23,2016

October 25, 2016

number theory

Problem Statement

The precent ages in years of two brothers

A

and

B

,and their father

C

are three distinct positive integers

a ,b

and

c

respectively .Suppose

\frac{c-1}{b-1}

and

\frac{c+1}{b+1}

are two consecutive integers , and

a+b+c\le 150

and

\frac{c+1}{b+1}

are two consecutive integers . If

a+b+c\le 150

, determine

a,b

and

c

.

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