You may also like

problem icon

Two Cubes

Two cubes, each with integral side lengths, have a combined volume equal to the total of the lengths of their edges. How big are the cubes? [If you find a result by 'trial and error' you'll need to prove you have found all possible solutions.]

problem icon

Root to Poly

Find the polynomial p(x) with integer coefficients such that one solution of the equation p(x)=0 is $1+\sqrt 2+\sqrt 3$.

problem icon

Janine's Conjecture

Janine noticed, while studying some cube numbers, that if you take three consecutive whole numbers and multiply them together and then add the middle number of the three, you get the middle number. Does this always work? Can you prove or disprove this conjecture?

Common Divisor

Stage: 4 Challenge Level: Challenge Level:1

Why do this problem?
It gives practice in factorisation and an opportunity for learners to make and prove conjectures.

Possible approach
This problem makes a good lesson starter.

Key questions
What are the factors of $n^5 - n$?