problem
Euler's Totient Function
How many numbers are there less than $n$ which have no common factors with $n$?
By sketching a graph of a continuous increasing function, can you prove a useful result about integrals?
I am thinking of three sets of numbers less than 101. Can you find all the numbers in each set from these clues?
This activity creates an opportunity to explore all kinds of number-related patterns.
This problem offers you two ways to test reactions - use them to investigate your ideas about speeds of reaction.
The Egyptians expressed all fractions as the sum of different unit fractions. The Greedy Algorithm might provide us with an efficient way of doing this.
The farmers want to redraw their field boundary but keep the area the same. Can you advise them?