From 5fcf73a2409362c2bf9fcc0a83b3fb581e2b1b6d Mon Sep 17 00:00:00 2001
From: Giftpflanze <gifti@tools.wmflabs.org>
Date: Sat, 9 Sep 2023 01:17:31 +0200
Subject: [PATCH] Add project-euler.066

---
 extra/project-euler/066/066-tests.factor |  6 ++
 extra/project-euler/066/066.factor       | 71 ++++++++++++++++++++++++
 extra/project-euler/066/authors.txt      |  1 +
 3 files changed, 78 insertions(+)
 create mode 100644 extra/project-euler/066/066-tests.factor
 create mode 100644 extra/project-euler/066/066.factor
 create mode 100644 extra/project-euler/066/authors.txt

diff --git a/extra/project-euler/066/066-tests.factor b/extra/project-euler/066/066-tests.factor
new file mode 100644
index 0000000000..d1705a1028
--- /dev/null
+++ b/extra/project-euler/066/066-tests.factor
@@ -0,0 +1,6 @@
+! Copyright (C) 2023 Giftpflanze.
+! See https://factorcode.org/license.txt for BSD license.
+USING: tools.test project-euler.066 ;
+IN: project-euler.066.tests
+
+{ 661 } [ euler066 ] unit-test
diff --git a/extra/project-euler/066/066.factor b/extra/project-euler/066/066.factor
new file mode 100644
index 0000000000..91f322b9f0
--- /dev/null
+++ b/extra/project-euler/066/066.factor
@@ -0,0 +1,71 @@
+! Copyright (C) 2023 Giftpflanze.
+! See https://factorcode.org/license.txt for BSD license.
+USING: kernel math math.functions math.order
+project-euler.common ranges sequences ;
+IN: project-euler.066
+
+! https://projecteuler.net/problem=66
+
+! DESCRIPTION
+! -----------
+
+! Consider quadratic Diophantine equations of the form:
+! x² - Dy² = 1
+
+! For example, when D = 13, the minimal solution in x is
+! 649² - 13 × 180² = 1.
+
+! It can be assumed that there are no solutions in positive
+! integers when D is square.
+
+! By finding minimal solutions in x for D = {2, 3, 5, 6, 7}, we
+! obtain the following:
+! 3² - 2 × 2² = 1
+! 2² - 3 × 1² = 1
+! 9² - 5 × 4² = 1
+! 5² - 6 × 2² = 1
+! 8² - 7 × 3² = 1
+
+! Hence, by considering minimal solutions in x for D <= 7, the
+! largest x is obtained when D = 5.
+
+! Find the value of D <= 1000 in minimal solutions of x for
+! which the largest value of x is obtained.
+
+
+! SOLUTION
+! --------
+
+! https://www.isibang.ac.in/~sury/chakravala.pdf
+! N = D
+! x0 = p0 = [sqrt(N)]
+! q0 = 1
+! m0 = p0² - N
+! x' ≡ -x (mod |m|), x' < sqrt(N) < x'+|m|
+! p' = (px'+Nq)/|m|
+! q' = (p+x'q)/|m|
+! m' = (x'²-N)/m
+
+:: chakravala ( n x p q m -- n x' p' q' m' )
+    n sqrt ceiling >integer :> upper-bound
+    upper-bound m abs - :> lower-bound
+    x neg m abs rem :> reminder
+    lower-bound reminder - :> distance
+    reminder distance m abs / ceiling 0 max m abs * + :> x'
+    n
+    x'
+    p x' * n q * + m abs /
+    p x' q * + m abs /
+    x' sq n - m / ;
+
+:: minimal-x ( D -- x )
+    D sqrt floor >integer :> p0
+    p0 sq D - :> m0
+    D p0 p0 1 m0
+    [ dup 1 = ] [ chakravala ] do until 2drop 2nip ;
+
+: euler066 ( -- D )
+    1000 [1..b] [ perfect-square? ] reject
+    [ minimal-x ] supremum-by ;
+
+SOLUTION: euler066
diff --git a/extra/project-euler/066/authors.txt b/extra/project-euler/066/authors.txt
new file mode 100644
index 0000000000..305077512d
--- /dev/null
+++ b/extra/project-euler/066/authors.txt
@@ -0,0 +1 @@
+Giftpflanze
-- 
2.34.1