MathDB

Division with specific quotients and remainders

Source: Paraguayan National Olympiad 2011, Level 3, Problem 3

August 31, 2014

number theory proposednumber theory

Problem Statement

If number

\overline{aaaa}

is divided by

\overline{bb}

, the quotient is a number between

140

and

160

inclusively, and the remainder is equal to

\overline{(a-b)(a-b)}

. Find all pairs of positive integers

(a,b)

that satisfy this.