منابع مشابه
Diophantine approximation and Diophantine equations
The first course is devoted to the basic setup of Diophantine approximation: we start with rational approximation to a single real number. Firstly, positive results tell us that a real number x has “good” rational approximation p/q, where “good” is when one compares |x − p/q| and q. We discuss Dirichlet’s result in 1842 (see [6] Course N◦2 §2.1) and the Markoff–Lagrange spectrum ([6] Course N◦1...
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following result. THEOREM 1. The only (n,m)eZ with n^2 and m5=4 satisfying © = ( 7 ) a r e {n> m)=(2> 4)> (6> 6)> and (21> Our binomial diophantine equation represents an elliptic curve, since it can be rewritten as a quartic polynomial being a square. Indeed, on putting u = 2/i 1 and v = 2m 3, we see at once that Theorem 1 follows from the following result. THEOREM 2. The only (u, v) e Z with ...
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In this note, we mainly obtain the equation x2m − yn = z2 have finite positive integer solutions (x, y, z,m, n) satisfying x > y be two consecutive primes. Mathematics Subject Classification: 11A41; 11D41
متن کاملAbout a Diophantine Equation
In this paper we study the Diophantine equation x −6xy +5y = 16Fn−1Fn+1, where (Fn) n≥0 is the Fibonacci sequence and we find a class of such equations having solutions which are determined.
متن کاملperversity: a Diophantine perspective
trace function 45, 46-48, 50, 51, 56, 62, 64 adapted stratification 12, 24, 26, 37, 38, 46, 48, 63, 121, 408 additive character sums 2, 7, 8, 111-158, 161-183, 270-280, 427-428 analytic rank 8, 443, 444, 445, 447, 449, 451, 453 analytic rank, geometric see "geometric analytic rank" analytic rank, quadratic see "quadratic analytic rank" Analytic Rank Theorem 445, 450-454 approximate trace fu...
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ژورنال
عنوان ژورنال: Bulletin of the American Mathematical Society
سال: 1927
ISSN: 0002-9904
DOI: 10.1090/s0002-9904-1927-04315-4