Integer#congruum?: Add

lib/numb.rb

@@ -1,23 +1,24 @@
 # coding: utf-8
 
 libs = %w{abundancy abundant achilles almost_perfect amicable aspiring 
-          automorphic balanced_prime carmichael carol composite coprime 
-          core cototient cube d decagonal deficient dodecagonal dihedral_prime
-          dudeney economical emrip equidigital extravagant factorion fibonacci 
-          friendly frugal happy harshad heptagonal hexagonal highly_composite 
-          highly_abundant hilbert hyperperfect idoneal impolite integer_p 
-          interprime jacobsthal_lucas kaprekar keith knodel k_perfect kynea 
-          leonardo leyland lucas lucas_carmichael mersenne_prime minimal 
-          mms_pair mobius myriagonal narcissistic next_prev_prime n_gonal 
-          nivenmorphic noncototient nth_prime number_of_divisors octagonal 
-          ordinal ore parasitic pentagonal perfect perfect_power polite 
-          polydivisible powerful practical prime_count prime_signature 
-          primitive_pseudoperfect primorial pronic proth refactorable repunit 
-          rhonda rough self self_descriptive semiperfect semiprime 
-          smarandache_wellin smith smooth sophie_germain_prime sphenic square
-          square_free sublime sum_of_squares superabundant superperfect totient
-          triangular trimorphic undulating unitary_perfect unitary_divisor 
-          untouchable vampire weird zeisel
+          automorphic balanced_prime carmichael carol congruum composite 
+          coprime core cototient cube d decagonal deficient dodecagonal 
+          dihedral_prime dudeney economical emrip equidigital extravagant 
+          factorion fibonacci friendly frugal happy harshad heptagonal 
+          hexagonal highly_composite highly_abundant hilbert hyperperfect 
+          idoneal impolite integer_p interprime jacobsthal_lucas kaprekar 
+          keith knodel k_perfect kynea leonardo leyland lucas lucas_carmichael
+          mersenne_prime minimal mms_pair mobius myriagonal narcissistic 
+          next_prev_prime n_gonal nivenmorphic noncototient nth_prime 
+          number_of_divisors octagonal ordinal ore parasitic pentagonal 
+          perfect perfect_power polite polydivisible powerful practical 
+          prime_count prime_signature primitive_pseudoperfect primorial pronic 
+          proth refactorable repunit rhonda rough self self_descriptive 
+          semiperfect semiprime smarandache_wellin smith smooth 
+          sophie_germain_prime sphenic square square_free sublime 
+          sum_of_squares superabundant superperfect totient triangular 
+          trimorphic undulating unitary_perfect unitary_divisor untouchable 
+          vampire weird zeisel
 }
 
 class Integer

lib/numb/congruum.rb

@@ -0,0 +1,13 @@
+class Integer
+  def congruum?
+    # Fibonacci proved that h|24
+    # Fermat’s right triangle theorem shows h is not square
+    return false unless divides?(24) and not square?
+    h = self
+    (1..Math.sqrt(h)).any? do |n|
+      (n.succ..Math.sqrt(h)).any? do |m|
+        h == (4 * m * n) * (m**2 - n**2)
+      end
+    end
+  end
+end

spec/congruum_spec.rb

@@ -0,0 +1,20 @@
+describe Integer, "#congruum?" do
+  # A057102
+  @seq = [24,96,120,240,336,384,480,720,840,960,1320,1344,
+          1536,1920,1944,2016,2184,2520,2880,3360,3696,3840,
+          3960,4896,5280,5376,5544,6144,6240,6840,6864,7680,
+          7776,8064,8736,9240,9360,9720,10080,10296,10920,
+          11520,12144].to_seq
+
+  @seq.each do |n|
+    it "should return true for congruum #{n}" do
+      n.should be_congruum
+    end
+  end
+
+  @seq.invert.sample(10).each do |n|
+    it "should return false for non-congruum #{n}" do
+      n.should_not be_congruum
+    end
+  end
+end