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1. The class number of a number field is the cardinality of the ideal class group of the field. 2. In group theory, the class number is the number of conjugacy classes of a group. 3. Class number is the number of equivalence classes of binary quadratic forms of a given discriminant. 4. The class number problem. conductor
Tunnell's theorem states that supposing n is a congruent number, if n is odd then 2A n = B n and if n is even then 2C n = D n. Conversely, if the Birch and Swinnerton-Dyer conjecture holds true for elliptic curves of the form y 2 = x 3 − n 2 x {\displaystyle y^{2}=x^{3}-n^{2}x} , these equalities are sufficient to conclude that n is a ...
Number theory is a branch of pure mathematics devoted primarily to the study of the integers and arithmetic functions.German mathematician Carl Friedrich Gauss (1777–1855) said, "Mathematics is the queen of the sciences—and number theory is the queen of mathematics."
James Burton Ax (10 January 1937 – 11 June 2006) [1] was an American mathematician who made groundbreaking contributions in algebra and number theory using model theory.He shared, with Simon B. Kochen, the seventh Frank Nelson Cole Prize in Number Theory, which was awarded for a series of three joint papers [2] [3] [4] on Diophantine problems.
Most recently, in 2020, Benjamin Burton classified all prime knots up to 19 crossings (of which there are almost 300 million). [4] [5] Starting with three crossings (the minimum for any nontrivial knot), the number of prime knots for each number of crossings is 1, 1, 2, 3, 7, 21, 49, 165, 552, 2176, 9988, 46972, 253293, 1388705, ...
Prime number, prime power. Bonse's inequality; Prime factor. Table of prime factors; Formula for primes; Factorization. RSA number; Fundamental theorem of arithmetic; Square-free. Square-free integer; Square-free polynomial; Square number; Power of two; Integer-valued polynomial
In elementary number theory, the lifting-the-exponent lemma (LTE lemma) provides several formulas for computing the p-adic valuation of special forms of integers. The lemma is named as such because it describes the steps necessary to "lift" the exponent of p {\displaystyle p} in such expressions.
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