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Shlomi Fish committed a90ab2d

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+Consider the infinite polynomial series AF(x) = xF1 + x2F2 + x3F3 + ..., where Fk is the kth term in the Fibonacci sequence: 1, 1, 2, 3, 5, 8, ... ; that is, Fk = Fk−1 + Fk−2, F1 = 1 and F2 = 1.
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+For this problem we shall be interested in values of x for which AF(x) is a positive integer.
+Surprisingly AF(1/2) 	 =  	(1/2).1 + (1/2)2.1 + (1/2)3.2 + (1/2)4.3 + (1/2)5.5 + ...
+  	 =  	1/2 + 1/4 + 2/8 + 3/16 + 5/32 + ...
+  	 =  	2
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+The corresponding values of x for the first five natural numbers are shown below.
+x	AF(x)
+√2−1	1
+1/2	2
+(√13−2)/3	3
+(√89−5)/8	4
+(√34−3)/5	5
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+We shall call AF(x) a golden nugget if x is rational, because they become increasingly rarer; for example, the 10th golden nugget is 74049690.
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+Find the 15th golden nugget.
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