giles
36e02c906a
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Uses Euclid's formula: for coprime m > k of opposite parity, the
triple (m^2 - k^2, 2mk, m^2 + k^2) is a primitive Pythagorean.
let count_primitive_triples n =
let c = ref 0 in
for m = 2 to 50 do
let kk = ref 1 in
while !kk < m do
if (m - !kk) mod 2 = 1 && gcd m !kk = 1 then begin
let h = m * m + !kk * !kk in
if h <= n then c := !c + 1
end;
kk := !kk + 1
done
done;
!c
count_primitive_triples 100 = 16
The 16 triples include the classics (3,4,5), (5,12,13), (8,15,17),
(7,24,25), and end with (65,72,97).
134 baseline programs total.