He arrived at the military academy — where tuition now reaches $31,000 a year — for eighth grade in 1959 and remained for high school. Like all students at the Cornwall-on-Hudson, N.Y., campus, he wore a uniform, participated in marching drills and was expected to conform to a hierarchy imposed by instructors, some of whom had served in the military.

Despite sitting out Vietnam because of deferments followed by a high draft lottery number of 356 out of 366, Mr. Trump said that he endured the rigors of real military life.

“My number was so incredible and it was a very high draft number. Anyway so I never had to do that, but I felt that I was in the military in the true sense because I dealt with those people,” he told Mr. D’Antonio.

The author seemed taken aback by this claim. Not many of the academy’s alumni “would compare military school with actual military service,” he wrote. “But the assertion was consistent with the self-image Trump often expressed.”