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Question

If (5+26)n=m+f, where n and m are positive integers and 0 f < 1, then 11ff is equal to:


A

1m

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B

m

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C

m+1m

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D

m1m

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Solution

The correct option is B

m


We have 526=1(5+26)
Therefore, 0 < 5 - 26<1. Let F=(526)n. Then 0 < F < 1. Also,
m+f+F=(5+26)n+(526)n=2[C05n+C25n2(26)2+C45n4(26)4+]=2k
where k is some positive integer. Hence, f + F = 2k - m is a positive integer. Also, 0 < f + F < 2. Therefore, f + F = 1. Now,
11ff=1F(1F)=(5+26)n{1(526)n}=(5+26)n+(526)n1
= m + f + F - 1 = m


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