Displaying similar documents to “An elliptic curve having large integral points”

The integral points on elliptic curves y 2 = x 3 + ( 36 n 2 - 9 ) x - 2 ( 36 n 2 - 5 )

Hai Yang, Ruiqin Fu (2013)

Czechoslovak Mathematical Journal

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Let n be a positive odd integer. In this paper, combining some properties of quadratic and quartic diophantine equations with elementary analysis, we prove that if n > 1 and both 6 n 2 - 1 and 12 n 2 + 1 are odd primes, then the general elliptic curve y 2 = x 3 + ( 36 n 2 - 9 ) x - 2 ( 36 n 2 - 5 ) has only the integral point ( x , y ) = ( 2 , 0 ) . By this result we can get that the above elliptic curve has only the trivial integral point for n = 3 , 13 , 17 etc. Thus it can be seen that the elliptic curve y 2 = x 3 + 27 x - 62 really is an unusual elliptic curve which has large integral points. ...

On the diophantine equation w+x+y = z, with wxyz = 2 3 5.

L. J. Alex, L. L. Foster (1995)

Revista Matemática de la Universidad Complutense de Madrid

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In this paper we complete the solution to the equation w+x+y = z, where w, x, y, and z are positive integers and wxyz has the form 2 3 5, with r, s, and t non negative integers. Here we consider the case 1 < w ≤ x ≤ y, the remaining case having been dealt with in our paper: On the Diophantine equation 1+ X + Y = Z, This work extends earlier work of the authors in the field of exponential Diophantine equations.