give the general formulas for the integer solutions of x^2 + y^2 = z^2. what is x,y, and z when m=18 and n=11

The equation x^2 + y^2 = z^2 represents a Pythagorean triple, where x, y, and z are integers that satisfy the equation. The general formulas for generating integer solutions to this equation can be obtained as follows:

1. Choose any two positive integers m and n, where m > n.
2. Compute x = m^2 - n^2, y = 2mn, and z = m^2 + n^2.
3. The values of x, y, and z obtained in step 2 will form a set of integer solutions to the equation x^2 + y^2 = z^2.

Now, let's substitute m = 18 and n = 11 into these formulas and calculate the values of x, y, and z:

x = (18^2) - (11^2) = 324 - 121 = 203
y = 2 * 18 * 11 = 396
z = (18^2) + (11^2) = 324 + 121 = 445

Therefore, when m = 18 and n = 11, the values of x, y, and z are x = 203, y = 396, and z = 445, respectively.