describe Integer, "#modulo_order" do
  @seq = {
    # A002326 
    2 => [1,2,4,3,6,10,12,4,8,18,6,11,20,18,28,5,10,12,36,
          12,20,14,12,23,21,8,52,20,18,58,60,6,12,66,22,35,
          9,20,30,39,54,82,8,28,11,12,10,36,48,30,100,51,12,
          106,36,36,28,44,12,24,110,20,100,7,14,130,18,36,
          68,138,46,60,28],
    # A050975
    3 => [1,2,4,6,2,4,5,3,6,4,16,18,4,5,11,20,3,6,28,30,8,
          16,12,18,18,4,8,42,10,11,23,42,20,6,52,20,6,28,29,
          10,30,16,12,22,16,12,35,12,18,18,30,78,4,8,41,16,
          42,10,88,6,22,23,36,48,42,20,100,34,6,52,53,27,20,
          12],
    # A050976      
    4 => [1,2,3,3,5,6,2,4,9,3,11,10,9,14,5,5,6,18,6,10,7,6,
          23,21,4,26,10,9,29,30,3,6,33,11,35,9,10,15,39,27,
          41,4,14,11,6,5,18,24,15,50,51,6,53,18,18,14,22,6,
          12,55,10,50,7,7,65,9,18,34,69,23,30,14,21,74,15,
          12,10,26],
    # A050977      
    5 => [1,2,1,2,6,2,6,5,2,4,6,4,16,6,9,6,5,22,2,4,18,6,
          14,3,8,10,16,6,36,9,4,20,6,42,5,22,46,4,42,16,4,
          52,18,6,18,14,29,30,3,6,16,10,22,16,22,5,6,72,36,
          9,30,4,39,54,20,82,6,42,14,10,44,12,22,6,46,8,96,
          42,30,25,16],
    # A050978      
    6 => [1,2,10,12,16,9,11,5,14,6,2,4,40,3,23,14,26,10,58,
          60,12,33,35,36,10,78,82,16,88,12,9,12,10,102,106,
          108,112,11,16,110,25,126,130,18,136,23,60,14,37,
          150,6,156,22,27,83,156,43,10,178,60,4,80,19,96,14,
          198,14],
    # A050979      
    7 => [1,1,2,4,1,2,3,4,10,2,12,4,2,16,3,3,4,10,22,2,4,
          12,9,7,4,15,4,10,16,6,9,3,12,4,40,6,10,12,22,23,2,
          4,16,12,26,9,20,3,7,29,4,60,15,8,12,10,66,16,22,
          70,6,24,9,4,6,12,78,4,27,40,41,16,6,7,10,88,12,22,
          15,23,12],
    # A050980
    8 => [2,4,1,2,10,4,4,8,6,2,11,20,6,28,5,10,4,12,4,20,
          14,4,23,7,8,52,20,6,58,20,2,4,22,22,35,3,20,10,13,
          18,82,8,28,11,4,10,12,16,10,100,17,4,106,12,12,28,
          44,4,8,110,20,100,7,14,130,6,12,68,46,46,20,28,14,
          148,5],
    # A050981      
    9 => [1,1,2,3,1,2,5,3,3,2,8,9,2,5,11,10,3,3,14,15,4,8,
          6,9,9,2,4,21,5,11,23,21,10,3,26,10,3,14,29,5,15,8,
          6,11,8,6,35,6,9,9,15,39,2,4,41,8,21,5,44,3,11,23,
          18,24,21,10,50,17,3,26,53,27,10,6,56,22,14,29,24,
          5,5,15],
    # A002329
    10 =>[1,6,1,2,6,16,18,6,22,3,28,15,2,3,6,5,21,46,42,16,
          13,18,58,60,6,33,22,35,8,6,13,9,41,28,44,6,15,96,
          2,4,34,53,108,3,112,6,48,22,5,42,21,130],
  }

  @seq.each do |base, values|
    1.upto(100) do |n|
      mo = base.modulo_order(n)
      value = mo.zero? ? 0 : values.shift
      it "returns #{value} for the multiplicative order of base #{base} (mod #{n})" do
        mo.should == value
      end
      break if values.empty?
    end
  end
end