Data commit

Task/Pells-equation/C/pells-equation.c

@@ -0,0 +1,62 @@
+#include <math.h>
+#include <stdbool.h>
+#include <stdint.h>
+#include <stdio.h>
+
+struct Pair {
+    uint64_t v1, v2;
+};
+
+struct Pair makePair(uint64_t a, uint64_t b) {
+    struct Pair r;
+    r.v1 = a;
+    r.v2 = b;
+    return r;
+}
+
+struct Pair solvePell(int n) {
+    int x = (int) sqrt(n);
+
+    if (x * x == n) {
+        // n is a perfect square - no solution other than 1,0
+        return makePair(1, 0);
+    } else {
+        // there are non-trivial solutions
+        int y = x;
+        int z = 1;
+        int r = 2 * x;
+        struct Pair e = makePair(1, 0);
+        struct Pair f = makePair(0, 1);
+        uint64_t a = 0;
+        uint64_t b = 0;
+
+        while (true) {
+            y = r * z - y;
+            z = (n - y * y) / z;
+            r = (x + y) / z;
+            e = makePair(e.v2, r * e.v2 + e.v1);
+            f = makePair(f.v2, r * f.v2 + f.v1);
+            a = e.v2 + x * f.v2;
+            b = f.v2;
+            if (a * a - n * b * b == 1) {
+                break;
+            }
+        }
+
+        return makePair(a, b);
+    }
+}
+
+void test(int n) {
+    struct Pair r = solvePell(n);
+    printf("x^2 - %3d * y^2 = 1 for x = %21llu and y = %21llu\n", n, r.v1, r.v2);
+}
+
+int main() {
+    test(61);
+    test(109);
+    test(181);
+    test(277);
+
+    return 0;
+}