If you calculate what percent of your total household income is contributed by each of you, this percentage can be used to figure out the fair share no matter what the expense is.
Your total household income is just the sum of your income, so $104,000 + $45,700 = $149,700. Your boyfriend contributes $104,000 of the $149,700, which is about 69.5%. You contribute the difference, or 30.5%.
So, to pay fair shares of a $1,600 rent payment, your boyfriend would pay 69.5% of it, or $1112, and you would pay your 30.5%, or $488.
Edit to add: I just rounded the percentage to the nearest tenth, to make it simpler. This means that the share isn't *exactly* proportional, but I feel like most people would agree it is close enough. If you prefer an exact proportion, just don't convert to a percentage at all. Multiply the rent payment by the original ratio of contributed money to total income. For example, an exact proportion would mean that your boyfriend would pay ($104,000 / $149,700) × $1600 = $1111.56. (This isn't entirely accurate either, because the actual number of cents is 55.6446, but of course you can't pay in fractions of a cent, so $1111.56 is as close as you're going to get to a perfect proportional split.) You obviously would pay the difference here, or $488.44. My approximation is simpler and within a dollar. If that isn't precise enough, using the exact ratio is as close as you are going to be able to get.