How many noughts are at the end of these giant numbers?
Prove that if a^2+b^2 is a multiple of 3 then both a and b are multiples of 3.
Find the largest integer which divides every member of the
following sequence: 1^5-1, 2^5-2, 3^5-3, ... n^5-n.
Try some numbers first - are you convinced?
For part two-
Now try to write the product or quotient of two square numbers
in a general form - can you rewrite this expression so
that it is a (a number) squared?
For part three -
What are all the possibilities for the units digit when you
square any whole number?