I'm a bit depressed that worked so easily :(

I just could not come to that simple conclusion. Yes we did learn about 
OR, AND, and one other that escapes me. I though about that as well. 
Also setting the leap year ,it wouldn't work unless I implicitly set it 
to an integer. So my final code is:

puts 'Leap Year Calculator'
puts ' '
puts 'Enter the starting year.'
starting_year = gets.chomp
puts 'Enter the ending year.'
ending_year = gets.chomp
leap_year = starting_year.to_i + starting_year.to_i % 4

while leap_year.to_i <= ending_year.to_i
  if (leap_year % 100) != 0 || (leap_year % 400) == 0
    puts leap_year
  end
  leap_year = leap_year.to_i + 4
end

Sobering :(

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