Pythagorean Pairs Theorem

This Theorem states that If a² + b² = c², then the pairs 

^{c+a & b}

^{c-a & b ( c<>a+1)}   

^{c+b & a}

^{c-b & a (c<>b+1)}

<sup>will always have at least one prime factor in common provided a,b,c belong to Integers(Z).

For Example...</sup>

  and so on.....     

Note: '<>' means 'Not Equal To'.