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A292872
Perfect n-th powers y^n (n >= 3) of the form x^2 + 2^a * 11^b (x >= 1, a, b >= 0, gcd(x, y) = 1).
0
27, 81, 125, 243, 729, 3375, 15625, 59049, 704969, 33698267, 41063625, 86938307, 100544625, 483736625, 163218919625
OFFSET
1,1
COMMENTS
Cangul, Demirci, Luca, Pinter and Soydan showed that there are no other terms.
LINKS
I. N. Cangul, M. Demirci, F. Luca, A. Pinter and G. Soydan, On the Diophantine Equation x^2 + 2^a 11^b = y^n, Fibonacci Quart. 48 (2010), 39-46.
EXAMPLE
a(8) = 59049 = 241^2 + 2^3 * 11^2 = 3^10 = 9^5
CROSSREFS
Cf. A295233 (2^a * 5^b instead of 2^a * 11^b).
Sequence in context: A129254 A215782 A216438 * A057609 A255624 A008884
KEYWORD
nonn,fini,full
AUTHOR
Tomohiro Yamada, Nov 19 2017
STATUS
approved