problem 130

130.boo

@@ -0,0 +1,38 @@
+/*
+Like 132:
+
+R(k) can be writen as: (10^k-1) / (10-1).
+
+Knowing if R(k) is divisible by some number n is same as knowing if:
+
+(10^k-1)/9 mod n == 0
+or
+(10^k-1) mod (n*9) == 0
+or
+10^k mod n*9 == 1
+
+We just need to know, then, which are the 25 first composite numbers for which 
+R(k) is divisible by k-1.
+*/
+import System
+import System.Collections.Generic
+import System.Linq.Enumerable
+
+P = PrimeNumbers()
+
+def pow(a as int, n as int, mod as int):
+   r, p = (1L, cast(long, a))
+   while(n):
+      if n%2: r=(r*p)%mod
+      p=(p*p)%mod
+      n/=2
+
+   return r
+
+def have_property(n as int):
+    return not P.IsPrime(n) and pow(10, n-1, n*9) == 1
+
+answer = range(5, int.MaxValue).Where(have_property).Take(25).Sum()
+
+print answer
+assert answer == 149253

138.boo

@@ -31,22 +31,18 @@ import System
 import System.Linq.Enumerable
 import System.Math
 
-
-def abs(a as BigInteger, b as BigInteger) as (BigInteger):
-  return ((a, b) if a>=0 and b>=0 else (-a,-b))
-
 px, py = BigInteger(0), BigInteger(1L)
 lx, ly = BigInteger(0), BigInteger(-1L)
 
 answer = 0L
 for i in range(12):
-  px, py = -9*px -8*py -8, -10*px - 9*py -8
-  if px > 0 and py > 0:
-    answer += py
+    px, py = -9*px -8*py -8, -10*px - 9*py -8
+    if px > 0 and py > 0:
+        answer += py
 
-  lx, ly = -9*lx -8*ly +8, -10*lx - 9*ly +8
-  if lx > 0 and ly > 0:
-    answer += ly
+    lx, ly = -9*lx -8*ly +8, -10*lx - 9*ly +8
+    if lx > 0 and ly > 0:
+        answer += ly
 
 print answer
 assert answer == 1118049290473932L