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pythag[n_]:=Block[{soln=Solve[{a^2+b^2==c^2,a+b+c<=n,0<a<b<c},{a,b,c},Integers]},{Length[soln],Count[GCD[a,b]/.soln,1]}]
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pTiming[n_] := With[{comp = Timing@pythag@(10^n)},
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{HoldForm[10^n], comp[[2, 1]], comp[[2, 2]], Round@comp[[1]]}];
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{{"n", "Triples", "Primitives", "Timing(s)"}}~Join~(pTiming /@ Range@5) // Grid
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primitivePythag[p_] := Join @@ Table[If[CoprimeQ[m, n], {2 m n, m^2 - n^2, m^2 + n^2}, ## &[]],{m, 2, Floor @ Sqrt @ p},{n, 1 + m ~Mod~ 2, m, 2}] // Select[Total[#] <= p &] // Length
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ppTiming[n_] := With[{comp = Timing@primitivePythag@(10^n)},{HoldForm[10^n], comp[[2]], Round@comp[[1]]}];
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{{"n", "Primitives", "Timing(s)"}}~Join~(ppTiming /@ Range@9) // Grid
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