CTNT 2022 - Wieferich Primes (by Keith Conrad)

This video is one of the special guess talks or conference talks that took place during CTNT 2022, the Connecticut Summer School and Conference in Number Theory.
Note: not every special guest lecture or conference lecture was recorded.
More about CTNT: ctnt-summer.ma...
Notes:
1) at 25:51 and 26:30, "if 2^(p-1) = 1 mod p^2" in the lecture should be "a^(2-1) = 1 mod 2^2".
2) at 31:54, Euler settled Fermat's Last Theorem for p = 3, not for p = 5.
3) at 42:00, the congruence a^2 = 1 mod 8 for odd a should be a = 1 mod 8 for p = 2.