منابع مشابه
Equal sums of four seventh powers
In this paper, the method used to find the smallest, nontrivial, positive integer solution of a1 + a 7 2 + a 7 3 + a 7 4 = b 7 1 + b 7 2 + b 7 3 + b 7 4 is discussed. The solution is 149 + 123 + 14 + 10 = 146 + 129 + 90 + 15. Factors enabling this discovery are advances in computing power, available workstation memory, and the appropriate choice of optimized algorithms. Introduction Diophantine...
متن کاملSimultaneous equal sums of three powers
Using a result of Salberger [9] we show that the number of non-trivial positive integer solutions x0, . . . , x5 6 B to the simultaneous equations x0 + x c 1 + x c 2 = x c 3 + x c 4 + x c 5, x d 0 + x d 1 + x d 2 = x d 3 + x d 4 + x d 5, is o(B) whenever d > max{2, c}. Mathematics Subject Classification (2000): 11D45 (11D41, 11P05)
متن کاملOn equal sums of ninth powers
In this paper, we develop an elementary method to obtain infinitely many solutions of the Diophantine equation x1 + x 9 2 + x 9 3 + x 9 4 + x 9 5 + x 9 6 = y 9 1 + y 9 2 + y 9 3 + y 9 4 + y 9 5 + y 9 6 and we give some numerical results.
متن کاملOn Sums of Powers of Almost Equal Primes
We investigate the Waring-Goldbach problem of representing a positive integer n as the sum of s kth powers of almost equal prime numbers. Define sk = 2k(k − 1) when k > 3, and put s2 = 6. In addition, put θ2 = 19 24 , θ3 = 4 5 and θk = 5 6 (k > 4). Suppose that n satisfies the necessary congruence conditions, and put X = (n/s). We show that whenever s > sk and ε > 0, and n is sufficiently large...
متن کاملPlane curves in boxes and equal sums of two powers
Let F ∈ Z[x1, x2, x3] be an absolutely irreducible form of degree d, producing a plane curve in P. The central aim of this paper is to analyze the density of rational points on such curves, which are contained in boxes with unequal sides. We shall see below how such considerations may be used to obtain new paucity results for equal sums of two powers. Suppose that P = (P1, P2, P3) for fixed rea...
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ژورنال
عنوان ژورنال: Rocky Mountain Journal of Mathematics
سال: 2000
ISSN: 0035-7596
DOI: 10.1216/rmjm/1021477247