My first x^x congruence: x^x≡2 (mod5)

My first x^x congruence, x^x≡2 (mod5), probably the first one on YouTube, too! However, I do not know how to solve the general case, but I did manage to "solve" it and got the same answer as WolframAlpha. ---------------------------------------- Big thanks to my Patrons for the full-marathon support! Ben D, Grant S, Mark M, Phillippe S. Michael Z, Jan P. Devun C. Stefan C. Ethan BW Didion S. NN Minkyu Y Brandon F Levon M shortsleeve Jack P Gabriel G Yeeted C David H Mateo F Emma M Eden E Minicat Jose R Nicholas Fey Tyler B Lucas W Ahmet Ö An R Camila L Luupo Farrah Batman 1127 Mathguru Дмитрий П. Michelle L. Alin V. Archer. L Ali. Subotai B. Spencer A. Chris Jason B. Ou S. Nuddi M. Jackson M. Jordan T. Gregorio B. Omkar N. John D. Zero Jeffrey C J D Chaz W. Ryan Turbo S Arcana Rehan M ---------------------------------------- 💪 Support this channel and get my math notes by becoming a patron: https://www.patreon.com/blackpenredpen 🛍 Shop my math t-shirt & hoodies: https://amzn.to/3qBeuw6 ---------------------------------------- #blackpenredpen #math #calculus #apcalculus