Investigate how you can work out what day of the week your birthday will be on next year, and the year after...
The picture illustrates the sum 1 + 2 + 3 + 4 = (4 x 5)/2. Prove the general formula for the sum of the first n natural numbers and the formula for the sum of the cubes of the first n natural numbers.
Show that if three prime numbers, all greater than 3, form an
arithmetic progression then the common difference is divisible by
6. What if one of the terms is 3?
Note: if you have an iPod Touch, iPhone, or iPad, or have Safari on your phone, there's a webapp called 'Light Delights' that you can use instead of the machine below.