58, 76, 97, 104

4 files changed, 127 insertions, 0 deletions

diff --git a/euler104.py b/euler104.py
new file mode 100644
index 0000000..5ec15b4
--- /dev/null
+++ b/euler104.py
@@ -0,0 +1,35 @@
+#!/usr/bin/env python
+
+from math import log10,sqrt
+
+fn_1 = 1
+fn_2 = 1
+n = 3
+
+def pandigital(n):
+    a = [False] * 10
+    while n > 0:
+        t = n % 10
+        if t == 0:
+            return False
+        if a[t]:
+            return False
+        a[t] = True
+        n = n / 10
+    return True
+
+while True:
+    fn = (fn_1 + fn_2) % 1000000000
+    if fn > 100000000 and pandigital(fn):
+        # a[n] = pow((1+sqrt(5))/2, n)/sqrt(5) 
+        #      - pow((1-sqrt(5))/2, n)/sqrt(5)
+        log10_fn = n*log10((1+sqrt(5))/2) - log10(sqrt(5))
+        frac = log10_fn - int(log10_fn)
+        first9 = int(pow(10, frac)*100000000)
+        if pandigital(first9):
+            print(n)
+            break
+
+    fn_2 = fn_1
+    fn_1 = fn
+    n = n + 1
diff --git a/euler58.c b/euler58.c
new file mode 100644
index 0000000..ac46073
--- /dev/null
+++ b/euler58.c
@@ -0,0 +1,45 @@
+#include <stdio.h>
+
+/*
+ *   delta = 4n+4           delta = 4n+2
+ *                 5     3
+ *                   [1]
+ *                 7     9
+ *   delta = 4n+6           delta = 4n+8
+ */
+
+int isprime(int n)
+{
+	if (n == 1 || n % 2 == 0)
+		return 0;
+
+	for (int i = 3; i * i <= n; i += 2) {
+		if (n % i == 0)
+			return 0;
+	}
+
+	return 1;
+}
+
+int main()
+{
+	int ndiag = 5;
+	int nprime = 3;
+	int s[4] = {3, 5, 7, 9};
+	int n = 2;
+
+	while (nprime * 10 > ndiag) {
+		s[0] += n * 4 + 2;
+		s[1] += n * 4 + 4;
+		s[2] += n * 4 + 6;
+		s[3] += n * 4 + 8;
+		for (int i = 0; i < 4; i++) {
+			if (isprime(s[i]))
+				nprime++;
+		}
+		ndiag += 4;
+		n += 2;
+	}
+	int sidelen = n + 1;
+	printf("%d\n", sidelen);
+}
diff --git a/euler76.scm b/euler76.scm
new file mode 100644
index 0000000..2542356
--- /dev/null
+++ b/euler76.scm
@@ -0,0 +1,17 @@
+(define (sum_ways n)
+ (define (sw n min-n)
+  (cond 
+   [(> min-n n) 0]
+   [(> (* min-n 2) n) 1]
+   [else (+ (sw (- n min-n) min-n) (sw n (+ min-n 1)))]
+   )
+ )
+
+ (define (sw-iter sum i)
+  (if (> (* i 2) n) sum
+   (sw-iter (+ sum (sw (- n i) i)) (+ i 1))))
+
+ (sw-iter 0 1))
+
+(display (sum_ways 100))
+(newline)
diff --git a/euler97.c b/euler97.c
new file mode 100644
index 0000000..b0f55bc
--- /dev/null
+++ b/euler97.c
@@ -0,0 +1,30 @@
+#include <openssl/bn.h>
+
+static const unsigned char _7830457[3] = { 0x77, 0x7b, 0xb9 };
+static const unsigned char _2[1] = {2};
+static const unsigned char _28433[2] = {0x6f, 0x11};
+static const unsigned char _10000000000[5] = {0x02, 0x54, 0x0b, 0xe4, 0x00};
+
+int main()
+{
+	BIGNUM *b28433 = BN_bin2bn(_28433, 2, NULL);
+	BIGNUM *b2 = BN_bin2bn(_2, 1, NULL);
+	BIGNUM *b7830457 = BN_bin2bn(_7830457, 3, NULL);
+	BIGNUM *b10ten = BN_bin2bn(_10000000000, 5, NULL);
+
+	BN_CTX *ctx = BN_CTX_new();
+	BIGNUM *r = BN_new();
+	BIGNUM *r2 = BN_new();
+	BIGNUM *r3 = BN_new();
+	BN_mod_exp(r, b2, b7830457, b10ten, ctx);
+	BN_mul(r2, r, b28433, ctx);
+	BN_add(r3, r2, BN_value_one());
+	BN_mod(r, r3, b10ten, ctx);
+
+	unsigned char res[10];
+	int len = BN_bn2mpi(r, res);
+	for (int i = 0; i < len; i++)
+		printf("%02x", res[i]);
+
+	puts("");
+}