=(2^2- 1))(2^2+ 1)(2^4+ 1)...(2^2004+ 1)=(2^4- 1)(2^4+ 1)...(2^2004+ 1)

=(2^ 16- 1)(2^ 16+ 1)...(2^2004+ 1)=2^4008- 1

2.( 1 square +3 square +5 square +...99 square) -(2 square +4 square +6 square +...98 square)

= 1+3 square +5 square +...99 square) -(2 square +4 square +6 square +...98 square) =1+(3 2-2 2 2)+(5 2-4 2)+(.

= 1+2+3++4+5+……+99=( 1+98)*50=4950

If the square of x-the square of y =48, we get (x -y) (x+y) = 48 and x+y=4. We get x-y= 12 x=8 y=-4.

Then 3x+2y = 3 * 8+2 *(4)= 16.

4. If a-b=2, the squares of both sides are (a-b) 2 = 4a 2-2ab+b 2 = 4.

And the square of a+the square of b =4, then a1= 0b1=-2a2 = 2b2 = 0, so the 2005 power of a+the 2005 power of b =+/-2 2005.

The x power of 5.2 times the y power of 9 =2x9y. From the left, we can see that y can only be 2 (the x power mantissa of 2 cannot be 9 or 0).

And 2 times 9 squared x power = 2x 922 x power =2x9y/8 1, greater than 2000 /8 1 is about 25, so x=5.