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I have answered three questions, and that is enough,”Said his father, “don’t give yourself airs!“Do you think I can listen all day to such stuff?Be off, or I’ll kick you down stairs!”

— LEWIS CARROLL, Alice’s Adventures Under Ground (1864)

### Notes on the Exercises

1. An average problem for a mathematically inclined reader.

3. See W. J. LeVeque, Topics in Number Theory 2 (Reading, Mass.: Addison–Wesley, 1956), Chapter 3; P. Ribenboim, 13 Lectures on Fermat’s Last Theorem (New York: Springer-Verlag, 1979); A. Wiles, Annals of Mathematics (2) 141 (1995), 443–551.

### Section 5

1. Let p(1) . . . p(N) and q(1) . . . q(N) be different permutations satisfying the conditions, and let i be minimal with p(i) ≠ q(i). Then p(i) = q(j) for ...

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