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?