Pythagorean Triples

Every primitive Pythagorean triple has the form

(

2

m

-

2

n

,2mn,

2

m

+

2

n

)

where

m

and

n

are relatively prime integers of opposite parity with

m>n≥1

. We list all such triples whose parameters

(m,n)

are bounded above by max.

In[]:=

max=10;For [m=2, m<=max, m++, For [n=1, n<m, n++, If [GCD[m,n]==1 && Mod[m+n,2]==1, Print["The pair (m,n)=(",m,",",n, ") gives the primitive Pythagorean triple (",m^2-n^2,",",2*m*n,",",m^2+n^2,")."]]]]