Divisibility with sums and differences

Students will learn that if two numbers \(x\) and \(y\) are divisible by some number \(k,\) then \(x + y\) and \(x - y\) are also divisible by \(k.\) Students should also learn how multi-digit numbers can be represented algebraically. For example, a three-digit number can be represented as

$$100a + 10b + c$$ where \(a,\) \(b,\) and \(c,\) each represent a single digit. Conclude by giving your students this challenge.