Changes

'''Table legend''': Each triple is noted as either a PPT (Primitive Pythagorean Triple) or is noted by being related to some other lower m-value triple by one of two relationships.

'''Table legend''': Each triple is noted as either a PPT (Primitive Pythagorean Triple) or is noted by being related to some other lower m-value triple by one of two relationships.

* 4X, 9X, etc. is where the Euclid parameters are a simple multiple of some lower m-value cell (i.e. m and n have a common factor, i.e. a GCD greater than one) and thus the triple values are multiplied by the square of that factor.

* 4X, 9X, etc. is where the Euclid parameters are a simple multiple of some lower m-value cell (i.e. m and n have a common factor, i.e. a GCD greater than one) and thus the triple values are multiplied by the square of that factor.

* T2X indicates a "2X" relation with lower m-value cell. The relationship is that the lower m-value triple (a,b,c) results in this cell's values being (2b, 2a, 2c), i.e. all three triple values are doubled and a and b are transposed. If the lower-m value cell is <math>E(m,n)</math> then this new cell is <math>E(m+n, m-n)</math>. E.g. For, <maht>E(5,2)</math> which results in <math>(21,20,29)</math>, the T2X is <math>E(5+2, 5-2)</math> or <math>E(7,3)</math> resulting in <math>(40,42,58)</math>. When searching for the lower m-value cell, one can use the inverse formula: <math>E((m+n)/2, (m-n)/2)</math>. E.g. when starting with <math>E(7,3)</math> and looking backwards, one finds <math>E((7+3)/2,(7-3)/2))</math> or just <math>E(5,2)</math>. In this case, the higher m-value parameters must be either both even or both odd.

* T2X indicates a "2X" relation with lower m-value cell. The relationship is that the lower m-value triple (a,b,c) results in this cell's values being (2b, 2a, 2c), i.e. all three triple values are doubled and a and b are transposed. If the lower-m value cell is <math>E(m,n)</math> then this new cell is <math>E(m+n, m-n)</math>. E.g. For, <math>E(5,2)</math> which results in <math>(21,20,29)</math>, the T2X is <math>E(5+2, 5-2)</math> or <math>E(7,3)</math> resulting in <math>(40,42,58)</math>. When searching for the lower m-value cell, one can use the inverse formula: <math>E((m+n)/2, (m-n)/2)</math>. E.g. when starting with <math>E(7,3)</math> and looking backwards, one finds <math>E((7+3)/2,(7-3)/2))</math> or just <math>E(5,2)</math>. In this case, the higher m-value parameters must be either both even or both odd.

See the next section for comments on the n=1 column and the n=m-1 diagonal.

See the next section for comments on the n=1 column and the n=m-1 diagonal.