We have seen textbooks that only gives solutions to odd-numbered exercises. But have you seen a number theory text with the following exercises?
1) Prove that [tex]x^3 + y^3 = z^3[/tex] has no non-trivial solutions in integers.
2) Prove that [tex]x^n + y^n = z^n[/tex] has no non-trivial solutions in integers, for all [tex]n \ge 3[/tex]
That’s actually apocryphal. Another story which appeared in George Dantzig’s obituary, tells of how he arrived late for a class one day to find two problems on the board. Thinking these were homework, he went back and solved them.
“The problems seemed to be a little harder to do than usual,” he said.
Turned out these two were open problems in statistical theory. (Note: I somehow remembered the protagonist as Paul Cohen.)
So perhaps it’s not too far-fetched to find the following exercise in Lang’s Complex Analysis. I checked my copy and it is a real-ly there!