Question

- n,x and y are integers, greater than zero

how many solutions (x,y) has the below equation ?

x^2 -y^2 = 10^n

Answer 1

@ganeshie8 what is your opinion about this please ? ty.

Answer 2

we can rewriting

x^2 -y^2 = (x-y)(x+y)

and

10^n = 2^n *5^n

Answer 3

I think it is only 1 solution since it is a hyperbola
\[\dfrac{x^2}{10^n}-\dfrac{y^2}{10^n}=1\]
when y=0, \(x^2=10^n\rightarrow x=\pm 10^{n/2}\)

and it is only one solution for the hyperbola.