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  2. Diophantine approximation - Wikipedia

    en.wikipedia.org/wiki/Diophantine_approximation

    The first problem was to know how well a real number can be approximated by rational numbers. For this problem, a rational number p/q is a "good" approximation of a real number α if the absolute value of the difference between p/q and α may not decrease if p/q is replaced by another

  3. Proof that e is irrational - Wikipedia

    en.wikipedia.org/wiki/Proof_that_e_is_irrational

    More generally, e q is irrational for any non-zero rational q. [13] Charles Hermite further proved that e is a transcendental number, in 1873, which means that is not a root of any polynomial with rational coefficients, as is e α for any non-zero algebraic α. [14]

  4. Euler's sum of powers conjecture - Wikipedia

    en.wikipedia.org/wiki/Euler's_sum_of_powers...

    In number theory, Euler's conjecture is a disproved conjecture related to Fermat's Last Theorem.It was proposed by Leonhard Euler in 1769. It states that for all integers n and k greater than 1, if the sum of n many k th powers of positive integers is itself a k th power, then n is greater than or equal to k:

  5. Ring of integers - Wikipedia

    en.wikipedia.org/wiki/Ring_of_integers

    It is the ring of integers in the number field () of Gaussian rationals, consisting of complex numbers whose real and imaginary parts are rational numbers. Like the rational integers, [] is a Euclidean domain. The ring of integers of an algebraic number field is the unique maximal order in the field. It is always a Dedekind domain. [4]

  6. Millennium Prize Problems - Wikipedia

    en.wikipedia.org/wiki/Millennium_Prize_Problems

    The other six Millennium Prize Problems remain unsolved, despite a large number of unsatisfactory proofs by both amateur and professional mathematicians. Andrew Wiles , as part of the Clay Institute's scientific advisory board, hoped that the choice of US$ 1 million prize money would popularize, among general audiences, both the selected ...

  7. Today’s NYT ‘Strands’ Hints, Spangram and Answers for ...

    www.aol.com/today-nyt-strands-hints-spangram...

    According to the New York Times, here's exactly how to play Strands: Find theme words to fill the board. Theme words stay highlighted in blue when found.

  8. 10 Healthy New Year’s Resolutions for 2025

    www.aol.com/10-healthy-resolutions-2025...

    Guidelines suggest getting at least 150 to 300 minutes (2.5 to five hours) of moderate-intensity aerobic exercise each week. Or at least 75 to 150 minutes (one hour 15 minutes to 2.5 hours) of ...

  9. Glossary of arithmetic and diophantine geometry - Wikipedia

    en.wikipedia.org/wiki/Glossary_of_arithmetic_and...

    The abc conjecture of Masser and Oesterlé attempts to state as much as possible about repeated prime factors in an equation a + b = c. For example 3 + 125 = 128 but the prime powers here are exceptional. Arakelov class group The Arakelov class group is the analogue of the ideal class group or divisor class group for Arakelov divisors. [3 ...

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