A284056 Array of complete solutions to the Diophantine equation x^2 + 5^a*11^b = y^3 read by rows (see comment).

0, 1, 4, 3, 0, 1, 58, 15, 0, 2, 2, 5, 0, 3, 9324, 443, 1, 1, 3, 4, 1, 1, 419, 56, 2, 3, 968, 99, 3, 1, 37, 14, 5, 5, 36599, 1226

Offset

1,3

Comments

The complete solution (a,b,x,y) to the Diophantine equation x^2 + 5^a*11^b = y^3

for x, y>= 1, gcd(x,y)=1, a,b>0:

(a, b, x, y)

(0, 1, 4, 3)

(0, 1, 58, 15)

(0, 2, 2, 5)

(0, 3, 9324, 443)

(1, 1, 3, 4)

(1, 1, 419, 56)

(2, 3, 968, 99)

(3, 1, 37, 14)

(5, 5, 36599, 1226)

Links

Table of n, a(n) for n=1..36.

Gökhan Soydan and Nikos Tzanakis, Complete solution of the Diophantine Equation x^2+5^a*11^b=y^n, arXiv:1703.04950 [math.NT], 2017; Bull. Hellenic Math. Soc. 60 (2016), 125-151.

Crossrefs

Sequence in context: A152148 A270708 A198261 * A338149 A338145 A296002

Adjacent sequences: A284053 A284054 A284055 * A284057 A284058 A284059

Keyword

nonn,fini,full,tabf

Author

Zak Seidov, Mar 19 2017

Status

approved