Divisibility

problem
LCM Sudoku

Age

14 to 16

Challenge level

Here is a Sudoku with a difference! Use information about lowest common multiples to help you solve it.
problem
Latin numbers

Age

14 to 16

Challenge level

Can you create a Latin Square from multiples of a six digit number?
problem
Obviously?

Age

14 to 18

Challenge level

Find the values of n for which 1^n + 8^n - 3^n - 6^n is divisible by 6.
problem
Prime AP

Age

16 to 18

Challenge level

What can you say about the common difference of an AP where every term is prime?
problem
Dirisibly yours

Age

16 to 18

Challenge level

Find and explain a short and neat proof that 5^(2n+1) + 11^(2n+1) + 17^(2n+1) is divisible by 33 for every non negative integer n.