If given a primitive triangle , we know that one of and is equal to and the other equals where and are relatively prime, positive integers, , and . But, how do we determine which of and equals ?

. Either or . If then . Therefore .

and

and

and |

and

and

and

Then

Let and . Then

and

Hence, we have,

and |

is a primitive 120 degree triangle. . Therefore . So,

Hence , , and .

is primitive. . Therefore . Thus

Hence , , and .

is a primitive 120 degree triangle. . Therefore . So,

Hence

and

is primitive. . Therefore . Thus

Hence

and