Drag the text box when it gets in the way.
Known elements in a pattern can be used to predict other elements. By eliminating either x or y from the latter, and substituting the result into the former, we get a quadratic equation in one variable with integer coefficients.
An example that follows all of these rules for a Pythagorean triple is the triple 5, 12, This equation is like the one given by Pythagoras, but it is different since each term is squared. We have just seen that if f is any prime factor of r, then f[IMAGE] is a factor of r, and this means that r is a square number.
Relative to the grid of the applet's coordinate axes, pixels are located at the points with rational coordinates with the denominator always equal to the number of pixels between two ticks on either axis.
This means that there is no whole number except 1 which is a factor of each of a,b,c for otherwise, we could reduce the triangle still further.