A related conjecture from Euler

Noam Elkies gave a counterexample, namely . Subsequently, Roger Frye found the absolutely smallest solution by (more or less) brute force: it is . "Several years", Math. Comp. 51 (1988) 825-835.

This synopsis is quite brief. A full survey would run too many pages.

**References**

*[1] J.P.Butler, R.E.Crandall,& R.W.Sompolski,* **Irregular Primes to One Million.** *Math. Comp.,* 59 (October 1992) pp. 717-722.

*Fermat's Last Theorem, A Genetic Introduction to Algebraic Number
Theory.* *H.M. Edwards.* Springer Verlag, New York, 1977.

*Thirteen Lectures on Fermat's Last Theorem.* *P. Ribenboim.* Springer Verlag, New York, 1979.

*Number Theory Related to Fermat's Last Theorem.* *Neal Koblitz, editor.* Birkhäuser Boston, Inc., 1982, ISBN 3-7643-3104-6

Mon Feb 23 16:26:48 EST 1998