Nonlinear Diophantine equation 11 x +13 y = z 2
نویسندگان
چکیده
منابع مشابه
ON THE DIOPHANTINE EQUATION x + y = 2pz
We show, if p is prime, that the equation xn + yn = 2pz2 has no solutions in coprime integers x and y with |xy| ≥ 1 and n > p132p , and, if p 6= 7, the equation xn + yn = pz2 has no solutions in coprime integers x and y with |xy| ≥ 1 and n > p12p .
متن کاملThe Diophantine equation f(x) = g(y)
have finitely or infinitely many solutions in rational integers x and y? Due to the classical theorem of Siegel (see Theorem 10.1 below), the finiteness problem for (1), and even for a more general equation F (x, y) = 0 with F (x, y) ∈ Z[x, y], is decidable (). One has to: • decompose the polynomial F (x, y) into Q-irreducible factors; • for those factors which are not Q-reducible, determine th...
متن کاملON THE DIOPHANTINE EQUATION x p − x = y q −
We consider the diophantine equation (∗) x − x = y − y in integers (x, p, y, q). We prove that for given p and q with 2 ≤ p < q (∗) has only finitely many solutions. Assuming the abcconjecture we can prove that p and q are bounded. In the special case p = 2 and y a prime power we are able to solve (∗) completely.
متن کاملOn the Diophantine Equation x^6+ky^3=z^6+kw^3
Given the positive integers m,n, solving the well known symmetric Diophantine equation xm+kyn=zm+kwn, where k is a rational number, is a challenge. By computer calculations, we show that for all integers k from 1 to 500, the Diophantine equation x6+ky3=z6+kw3 has infinitely many nontrivial (y≠w) rational solutions. Clearly, the same result holds for positive integers k whose cube-free part is n...
متن کاملON SOLVING THE DIOPHANTINE EQUATION x 3 + y 3 + z 3 = k ON A VECTOR COMPUTER
Recently, the first author has proposed a new algorithm for solving the Diophantine equation x3 + y3 + z3 = k , where k is a given nonzero integer. In this paper we present the detailed versions of this algorithm for some values of k given below, and we describe how we have optimized and run the algorithm on a Cyber 205 vector computer. A vectorized version of the Euclidean algorithm was writte...
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: IOP Conference Series: Materials Science and Engineering
سال: 2018
ISSN: 1757-8981,1757-899X
DOI: 10.1088/1757-899x/332/1/012004