University of Strathclyde mathematician Adam McBride recalls that in his student days a particular teacher used to present a weekly puzzle. One of these baffled him:
Find positive integers a, b, and c, all different, such that a3 + b3 = c4.
“The previous puzzles had been relatively easy but this one had me stumped,” he wrote later. He created three columns headed a3, b3, and c4 and spent hours looking for a sum that would work. On the night before the deadline, he found one: 703 + 1053 = 354.
“This shows how sad a person I was! However, I then realised also how stupid I had been. I had totally missed the necessary insight.” What was it?