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 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 .

The number of positive integral pairs (x, y) satisfying the equation x^(2) - y^(2) = 3370 is :

The number of ordered pairs (x,y) of positive integers satisying 2^(x) + 3^(y) = 5^(xy) is

The number of pairs (x,y) of positive integers such that sqrt(x)+sqrt(y)=sqrt(1980)

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