Can you describe this route to infinity? Where will the arrows take you next?
Where we follow twizzles to places that no number has been before.
Arrow arithmetic, but with a twist.
A loopy exploration of z^2+1=0 (z squared plus one) with an eye on
winding numbers. Try not to get dizzy!
Make the twizzle twist on its spot and so work out the hidden link.
Add powers of 3 and powers of 7 and get multiples of 11.
When is $7^n + 3^n$ a multiple of 10? Can you prove the result by two different methods?
Investigate powers of numbers of the form (1 + sqrt 2).
Both Tiffany and Andrei sent in clear solutions to this problem.
Go to last month's problems to see more solutions.
In this article we shall consider how to solve problems such as
"Find all integers that leave a remainder of 1 when divided by 2,
3, and 5."
This Sudoku puzzle can be solved with the help of small clue-numbers on the border lines between pairs of neighbouring squares of the grid.