Understanding Integer Expressions and Divisibility

The video tutorial explores a mathematical problem involving three integers a, b, and c, all greater than zero. It is given that the expression (a + b) / c is an integer, and a is a multiple of c. The main question posed is whether b must also be a multiple of c. The video encourages viewers to pause and think about the problem before proceeding with the solution. The solution involves breaking down the expression into parts and logically deducing that b must indeed be a multiple of c for the entire expression to remain an integer.

What are the given conditions for the integers a, b, and c?

• They are all less than 0.

• They are all prime numbers.

• They are all greater than 0.

• They are all equal to 0.

What is the main question we need to solve regarding b?

• Is b a prime number?

• Is b greater than a?

• Does b have to be a multiple of c?

• Is b less than c?

How can we rewrite the expression (a + b) / c?

• a + b*c

• a - b/c

• a*b/c

• a/c + b/c

What do we know about a/c in the expression?

• It is a fraction.

• It is a non-integer.

• It is an integer.

• It is a negative number.

Why must b/c be an integer?

• Because the entire expression must be an integer.

• Because c is a prime number.

• Because b is greater than c.

• Because a/c is a fraction.

What conclusion can we draw about b?

• b is equal to c.

• b is a prime number.

• b must be a multiple of c.

• b is less than a.