A295233 Perfect n-th powers y^n (n >= 3) of the form x^2 + 2^a * 5^b (x, a, b >= 1, gcd(x, y) = 1).

81, 729, 1331, 6561, 68921, 161051, 2146689, 315821241

Offset

1,1

Comments

Luca and Togbe showed that there are no other terms.

Links

Table of n, a(n) for n=1..8.

F. Luca and A. Togbe, On the Diophantine Equation x^2 + 2^a 5^b y^n, Int. J. Number Theory 4 (2008), 973-979.

Example

a(2) = 729 = 23^2 + 2^3 * 5^2 = 3^6 = 9^3, a(8) = 315821241 = 17771^2 + 2^9 * 5^2 = 681^3.

Crossrefs

Sequence in context: A133549 A235946 A090257 * A271829 A066431 A206086

Adjacent sequences: A295230 A295231 A295232 * A295234 A295235 A295236

Keyword

nonn,fini,full

Author

Tomohiro Yamada, Nov 18 2017

Status

approved