Modular arithmetic with Fermat and Euler | Data Structures in Mathematics Math Foundations 197
There are two important theorems that make the job of understanding powers in modular arithmetic much simpler. These go back to Fermat and Euler. We apply these to the nice problem of deciding z mod 13. Fermat's result helps us understand powers to a prime modulus. Euler's result relies on understanding the interesting Euler phi function, and is a generalization of Fermat's. As usual we like to illustrate theorems with explicit examples. ************ Research Gate page: https://www.researchgate.net/profile/... Blog: http://njwildberger.com/ Online courses at openlearning.com (currently Algebraic Calculus One): https://www.openlearning.com/courses/... Please join us for an exciting new approach to one of mathematics' most important subjects! Patreon: / njwildberger Your support would be much appreciated. Wild Egg Maths YT channel: https://www.youtube.com/channel/UCriF... Insights into Mathematics Playlists: • The Algebra of Boole, Logic and Circuit An... (31 videos) • Box Arithmetic: a new framework for Mathem... (18 videos) • Hypergroups and Diffusion Symmetry: an int... (6 videos) • Rational Trigonometry for maths, physics a... (4 videos) • Sociology and Pure Maths (44 videos) • Old Babylonian mathematics and Plimpton 322 (8 videos) • Math Foundations (226 videos) • Math Seminars N J Wildberger (26 videos) • Math History (ancient to modern) (45 videos) • Geometric Linear Algebra (43 videos) • Algebraic Topology (40 videos) • Universal Hyperbolic Geometry (55 videos) • Differential Geometry (34 videos) • Elementary Probability and Statistics (8 videos) • Math Terminology for Incoming Uni Students (9 videos) • Famous Math Problems ( 46 videos) • Elementary Mathematics Explained (K-6) (40 videos) • Ancient Mathematics and insights of Howard... (7 videos) • Wild West Banking: A mathematician goes We... (7 videos) • Playing Go: the ancient oriental board game (19 videos) • Maths and Music (21 videos) • Year 9 Mathematics (review fractions, deci... (10 videos) • Wild Trig: An introduction to Rational Tri... (94 videos) Wild Egg Maths Playlists: • Intro to Algebraic Calculus with Box Arith... (4 videos) • Classical to Quantum (for Members) (64 videos) • Solving Polynomial Equations and the Geode... (45 videos) • De Casteljau Bezier curves and associated ... (20 videos) • Exploring q-series (for Members) (8 videos) • Six: A mathematical exploration (9 videos) • Algebraic Calculus One: a new foundation f... (52 videos) • Advice to prospective research mathematici... (9 videos) • The Hexagrammum Mysticum: a Geometric Gem ... (14 videos) • Algebraic Calculus Two (8 videos) • Special (Polynomial) Functions and Maxel N... (25 videos) • Dynamics on Graphs: The ADE Phenomenon & B... (30 videos)
