Long List
Weekly Problem 47 - 2017
How many numbers do I need in a list to have two squares, two primes and two cubes?
How many numbers do I need in a list to have two squares, two primes and two cubes?
Age
14 to 16
Challenge level
Problem
I want to write a list of integers containing two square numbers, two prime numbers and two cube numbers. What is the smallest number of integers that could be in my list?
If you liked this problem, here is an NRICH task that challenges you to use similar mathematical ideas.
Student Solutions
Answer: 4 numbers
The 2 squares and 2 cubes cannot be prime
Could the squares also be cubes?
$(2\times2\times2)\times(2\times2\times2) = (2\times2)\times(2\times2)\times(2\times2)$ is a square and a cube, so yes
So you need 2 primes and 2 square-cubes