prove or disprove:
a) any positive integer can be written as the sum of the squares of two integers
b) for every integer n, the number 3(n2 + 2n + 3) ? 2n2 is a perfect square

Step-by-step explanation:

a). Let

Now since is a square of an integer, its value is 0.

Therefore, ≥ 0, since x is an integer

where = 1,2,3,...

and x = 1

But as x = ,... cannot be integer

∴

              = 1.732      which is not an integer

Thus, any positive integer cannot be written as the sum of the squares of the two integers.

b). Let n be an integer

∴

On solving we get,

which is a perfect square

Hence proved.

529 and 531

step-by-step explanation: