The number of solutions of `2^(2x)-3^(2y)=55`, in which x and y are integers, is

The number of solutions (x, y) where x and y are integers, satisfying 2x^(2) + 3y^(2) + 2x + 3y=10 is:

The number of solution of y'=(x+1)/(x-1),y(1)=2 , is

The number of solutions (x,y) where x and y are integers,satisfying 2x^(2)+3y^(2)+2x+3y=10 is

The number of solutions of the equation 2x + y = 40 where both x and y are positive integers and x le y .

Find the total number of solutions to the equation x^2 + y^2 = 2015 where both x and y are integers.

The number of common solutions for 3x+2y=18 and 5x+4y=3 is

The number of pairs of positive integers (x,y) where x and y are prime numbers and x^(2)-2y^(2)=1 , is

The number of pairs of positive integers (x,y) where x and y are prime numbers and x^(2)-2y^(2)=1 , is