OFFSET
1,1
COMMENTS
It is an open question whether any two distinct Pythagorean triples can have the same product of their sides.
EXAMPLE
a(1)=3*4*5=60; a(2)=5*12*13=780 (rather than 6*8*10=480, which would not be primitive).
MATHEMATICA
k=17000000; lst={}; Do[Do[If[IntegerQ[a=Sqrt[c^2-b^2]]&&GCD[a, b, c]==1, If[a>=b, Break[]]; x=a*b*c; If[x<=k, AppendTo[lst, x]]], {b, c-1, 4, -1}], {c, 5, 700, 1}]; Union@lst (* Vladimir Joseph Stephan Orlovsky, Sep 05 2009 *)
With[{nn=50}, Take[(Times@@#)Sqrt[#[[1]]^2+#[[2]]^2]&/@Union[Sort/@ ({Times@@#, (Last[#]^2-First[#]^2)/2}&/@(Select[Subsets[Range[1, nn+1, 2], {2}], GCD@@#==1&]))]//Union, nn]] (* Harvey P. Dale, Jun 08 2018 *)
CROSSREFS
KEYWORD
nonn
AUTHOR
Henry Bottomley, Jul 26 2001
STATUS
approved