Each time, he requested an extension to file his 1040; and each time, he made the required payment to the I.R.S. for income taxes he might owe — $1 million for 2016 and $4.2 million for 2017. But virtually all of that liability was washed away when he eventually filed, and most of the payments were rolled forward to cover potential taxes in future years.

To cancel out the tax bills, Mr. Trump made use of $9.7 million in business investment credits, at least some of which related to his renovation of the Old Post Office hotel, which qualified for a historic-preservation tax break. Although he had more than enough credits to owe no taxes at all, his accountants appear to have carved out an allowance for a small tax liability for both 2016 and 2017.

When they got to line 56, the one for income taxes due, the amount was the same each year: $750.