Question 47
A positive integer is written on a blackboard. Each minute Andrew looks at his clock and adds the number of minutes the clock is showing (an integer between $0$ and $59$) to the number written on the blackboard.
a) Prove that at some moment a composite number will be written on the blackboard.
b) Will necessarily a number divisible by $5$ be written?
a) Prove that at some moment a composite number will be written on the blackboard.
b) Will necessarily a number divisible by $5$ be written?