Linear transformation of Pythagorean triples into Pythagorean triples
For any integer q, If x^2 + y^2 = z^2 Then ((2q^2 -1)x -(2q)y + (2 q^2 )z)^2 +((2q )x -(1 )y + (2q )z)^2 =((2q^2 )x -(2q)y + (2q^2+1)z)^2 Proof: ((2q^2 -1)x -(2q)y + (2 q^2 )z)^2 +((2q )x -(1 )y + (2q )z)^2 -((2q^2 )x -(2q)y + (2q^2+1)z)^2 = ((2q^2-1)^2 + (2q)^2 - (2q^2)^2) x^2 +((2q)^2 + 1 -... Sign in to see full entry.