Powers of Two as Sums of Three Pell Numbers
نویسندگان
چکیده
منابع مشابه
On Powers as Sums of Two Cubes
In a paper of Kraus, it is proved that x 3 + y 3 = z p for p 17 has only trivial primitive solutions, provided that p satisses a relatively mild and easily tested condition. In this article we prove that the primitive solutions of x 3 + y 3 = z p with p = 4; 5; 7; 11; 13, correspond to rational points on hyperelliptic curves with Jaco-bians of relatively small rank. Consequently, Chabauty metho...
متن کاملRepdigits as sums of three Fibonacci numbers
In this paper, we find all base 10 repdigits which are sums of three Fibonacci numbers. AMS subject classifications: Primary 11D61; Secondary 11A67, 11B39
متن کاملPerfect Powers Expressible as Sums of Two Cubes
Let n ≥ 3. This paper is concerned with the equation a3 + b3 = cn, which we attack using a combination of the modular approach (via Frey curves and Galois representations) with obstructions to the solutions that are of Brauer–Manin type. We shall show that there are no solutions in coprime, non-zero integers a, b, c, for a set of prime exponents n having Dirichlet density 28219 44928 ≈ 0.628, a...
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 کاملSums of Three Squareful Numbers
We investigate the frequency of positive squareful numbers x, y, z 6 B for which x + y = z and present a conjecture concerning its asymptotic behaviour. Mathematics Subject Classification (2010). 11D45 (11P05, 14G05).
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: Taiwanese Journal of Mathematics
سال: 2017
ISSN: 1027-5487
DOI: 10.11650/tjm/7840