6

Part of 2013 Costa Rica - Final Round

Problems(1)

b/a= 6 if b is divisible by a, overline{ab}= (a + b)^2

Source: OLCOMA Costa Rica National Olympiad, Final Round, 2013 3.6

a

b

be positive integers (of one or more digits) such that

b

is divisible by

a

, and if we write

a

b

, one after the other in this order, we get the number

(a + b)^2

\frac{b}{a}= 6

number theoryDigitsdivisible