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Pythagorean triples: Difference between revisions
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return 0;
}</lang>output:<lang>Up to 100, there are 17 triples, of which 7 are primitive</lang>
Efficient method, generating primitive triples only as described in [[wp:Pythagorean_triple#Parent.2Fchild_relationships|the same WP article]]:<lang C>#include <stdio.h>
#include <stdlib.h>
#include <stdint.h>
/* should be 64-bit integers if going over 1 billion */
typedef unsigned long xint;
#define FMT "%lu"
xint total, prim, max_peri;
xint U[][9] = {{ 1, -2, 2, 2, -1, 2, 2, -2, 3},
{ 1, 2, 2, 2, 1, 2, 2, 2, 3},
{-1, 2, 2, -2, 1, 2, -2, 2, 3}};
void new_tri(xint in[])
{
int i;
xint t[3], p = in[0] + in[1] + in[2];
if (p > max_peri) return;
prim ++;
/* for every primitive triangle, its multiples would be right-angled too;
* count them up to the max perimeter */
total += max_peri / p;
/* recursively produce next tier by multiplying the matrices */
for (i = 0; i < 3; i++) {
t[0] = U[i][0] * in[0] + U[i][1] * in[1] + U[i][2] * in[2];
t[1] = U[i][3] * in[0] + U[i][4] * in[1] + U[i][5] * in[2];
t[2] = U[i][6] * in[0] + U[i][7] * in[1] + U[i][8] * in[2];
new_tri(t);
}
}
int main()
{
xint seed[3] = {3, 4, 5};
for (max_peri = 10; max_peri <= 100000000; max_peri *= 10) {
total = prim = 0;
new_tri(seed);
printf( "Up to "FMT": "FMT" triples, "FMT" primitives.\n",
max_peri, total, prim);
}
return 0;
}</lang>Output<lang>Up to 10: 0 triples, 0 primitives.
Up to 100: 17 triples, 7 primitives.
Up to 1000: 325 triples, 70 primitives.
Up to 10000: 4858 triples, 703 primitives.
Up to 100000: 64741 triples, 7026 primitives.
Up to 1000000: 808950 triples, 70229 primitives.
Up to 10000000: 9706567 triples, 702309 primitives.
Up to 100000000: 113236940 triples, 7023027 primitives.</lang>
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