Problem of the Week 2-28-19: Terms of an Arithmetic Sequence [Algebra]

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Advanced Knowledge Problem of the Week 2-26-19: Units in a Noncommutative Ring [Algebra]

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Problem of the Week 2-21-19: Functional Equation on Non-Negative Reals [Functional Equation]

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Advanced Knowledge Problem of the Week 2-19-19: Prime Divisor of Numerator [Algebra]

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Problem of the Week 2-14-19: Finding a Positive Integer Solution [Number Theory]

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Advanced Knowledge Problem of the Week 2-12-19: Graph with Different Degree Vertices [Graph Theory]

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Problem of the Week 2-7-19: Upper Bound of a Sum [Algebra]

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New Video Series on Number Theory

Prime Phyllotaxis Spiral

This series is for beginners in Number Theory. The series starts with an introduction to congruences. We review the basic properties of congruences and present the proofs of these properties. Once you become comfortable working with modular arithmetic, we introduce Fermat's Little Theorem and Euler's Theorem. We go over common applications of these theorems, such as solving linear congruences, finding the least positive residue and solving modular inverses. Then, we learn how to solve a set of congruences using the Chinese Remainder Theorem. We finish the series by discussing the order of integers and primitive prime roots.  

Advanced Knowledge Problem of the Week 2-5-19: Sum of Relatively Prime Integers [Number Theory]

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