Problem #PRU-100702

Problems Number Theory Divisibility Division with remainders. Arithmetic of remainders Division with remainder

Problem

We have two rectangles: the first one has sides of length \(a\) and \(c\), and the second rectangle has sides of length \(b\) and \(d\).

Imagine that the difference in their side lengths, i.e: \(a-b\) and \(c-d\) are both divisible by \(11\). Show that the difference in their areas, i.e: \(ac-bd\), is also divisible by \(11\).