Project Euler 45

project_euler_45.rb

def sq? n
  # ↓32bit整数の範囲ならとりあえずこれでOK
  Math.sqrt(n).round**2 == n
end

def project_euler_45 n=143
  loop do
    n += 1
    h = n * (2 * n - 1)
    next unless sq?(8 * h + 1)
    next unless sq?(24 * h + 1)
    next unless Math.sqrt(24 * h + 1).to_i % 6 == 5
    n3 = (Math.sqrt(8 * h + 1).to_i - 1) / 2
    n5 = (Math.sqrt(24 * h + 1).to_i + 1) / 6
    puts "T#{n3} = P#{n5} = H#{n} = #{h}"
    return h
  end
end

if $0 == __FILE__
  p project_euler_45
end