(i) If is a positive integer, such that is a perfect square, show that is the sum of two successive perfect squares.
(ii) If is a perfect square, show that is the sum of three perfect square.
(i)A square of an odd number
If then and that shows that is the square of an odd number.
Now consider that is the sum of two successive squares.
(ii) A number can be of the form
Square can thus be of the form :
So if a square then
Then n +1 is form (when 3n+1 is odd) or is form (when 3n+1 is even)