We look a few concepts and results from Number Theory that are commonly used in mathematics competitions. Solutions to two examples are also given, including one to the 1985 AIME. Please Subscribe: https://www.youtube.com/michaelpennmath?sub_confirmation=1 Merch: https://teespring.com/stores/michael-penn-math Personal Website: http://www.michael-penn.net Randolph College Math: http://www.randolphcollege.edu/mathematics/ Randolph College Math and Science on Facebook: https://www.facebook.com/randolph.science/ Research Gate profile: https://www.researchgate.net/profile/Michael_Penn5 Google Scholar profile: https://scholar.google.com/citations?user=W5wkSxcAAAAJ&hl=en If you are going to use an ad-blocker, considering using brave and tipping me BAT! https://brave.com/sdp793 Buy textbooks here and help me out: https://amzn.to/31Bj9ye Buy an amazon gift card and help me out: https://amzn.to/2PComAf Books I like: Sacred Mathematics: Japanese Temple Geometry: https://amzn.to/2ZIadH9 Electricity and Magnetism for Mathematicians: https://amzn.to/2H8ePzL Abstract Algebra: Judson(online): http://abstract.ups.edu/ Judson(print): https://amzn.to/2Xg92wD Dummit and Foote: https://amzn.to/2zYOrok Gallian: https://amzn.to/2zg4YEo Artin: https://amzn.to/2LQ8l7C Differential Forms: Bachman: https://amzn.to/2z9wljH Number Theory: Crisman(online): http://math.gordon.edu/ntic/ Strayer: https://amzn.to/3bXwLah Andrews: https://amzn.to/2zWlOZ0 Analysis: Abbot: https://amzn.to/3cwYtuF How to think about Analysis: https://amzn.to/2AIhwVm Calculus: OpenStax(online): https://openstax.org/subjects/math OpenStax Vol 1: https://amzn.to/2zlreN8 OpenStax Vol 2: https://amzn.to/2TtwoxH OpenStax Vol 3: https://amzn.to/3bPJ3Bn My Filming Equipment: Camera: https://amzn.to/3kx2JzE Lense: https://amzn.to/2PFxPXA Audio Recorder: https://amzn.to/2XLzkaZ Microphones: https://amzn.to/3fJED0T Lights: https://amzn.to/2XHxRT0 White Chalk: https://amzn.to/3ipu3Oh Color Chalk: https://amzn.to/2XL6eIJ