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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).
1

%I #13 Nov 21 2017 20:02:38

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

%N 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).

%C Luca and Togbe showed that there are no other terms.

%H F. Luca and A. Togbe, <a href="https://doi.org/10.1142/S1793042108001791">On the Diophantine Equation x^2 + 2^a 5^b y^n</a>, Int. J. Number Theory 4 (2008), 973-979.

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

%K nonn,fini,full

%O 1,1

%A _Tomohiro Yamada_, Nov 18 2017