Problem of the Week: 10-18-18: Prove that the Fraction is Irreducible [Number Theory]
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Problem of the Week: 09-06-18: Solving Linear Congruence using Fermat's Little Theorem [Number Theory]
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Advanced Knowledge Problem of the Week 7-5-18: Infinite Squares and Euler's Totient Function [Number Theory]
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Problem of the Week 7-3-18: Invariant Sums of Digits [Number Theory]
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Problem of the Week 6-26-18: Integers and Quartics [Number Theory]
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Problem of the Week 6-12-18: Making Polynomials Prime [Number Theory]
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Problem of the Week 5-29-18: Numbers with Certain Divisors [Number Theory]
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Problem of the Week 5-22-18: Integer Function [Number Theory]
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Problem of the Week 5-15-18: A Set of Integers [Number Theory]
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Advanced Knowledge Problem of the Week 5-10-18: How many prime factors? [Number Theory]
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Advanced Knowledge Problem of the Week 5-3-18: A Lack of Primitive Roots [Number Theory]
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Problem of the Week 5-1-18: Problem on Primality [Number Theory]
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Some History and Unsolved Problems in Number Theory
Number theory is a very old subject, which is concerned with the set of integers. Number theory started with the concept of integers and simple operations on the integers such as addition, subtraction, etc. Number theory of the greeks is primarily found in the works of Euclid and Plato. Indian mathematicians of antiquity such as Brahmagupta also made significant contributions (one of Brahmagupta's contributions was work on what is now known as Pell's equation). Pierre de Fermat was an important figure in number theory as well, he is responsible for Fermat's theorem as well as Fermat's Last Theorem (a problem which is now solved). Some additional major figures in early number theory were Leonhard Euler, Joseph-Louis Lagrange, and Carl Friedrich Gauss. Eventually number theory itself started to split into recognizable subbranches, two major ones being algebraic number theory and analytical number theory. Analytical number theory is concerned with the use of real and compl...
Problem of the Week 4-24-18: Board Covering [Number Theory]
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Problem of the Week 3-27-18: Area Parity [Number Theory]
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Problem of the Week 3-20-18: Same Last Three Digits [Number Theory]
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Advanced Knowledge Problem of the Week 3-16-18: Mobius Function Sums [Number Theory]
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Problem of the Week 3-6-18: Diophantine Equation/Prime Powers [Number Theory]
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Advanced Knowledge Problem of the Week 2-15-18: Modular Arithmetic and Factorials [Number Theory]
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Problem of the Week 2-6-18: Powers of Five [Number Theory]
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