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What is the smallest positive integer n such that, out of the n unit fractions 1/k where 1<=k<=n, exactly half of the fractions give a terminating decimal?

 

<= means less than or equal to

 Nov 29, 2019
 #1
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I think the smallest  positive integer = 10

1/2 ,  1/4,  1/5,  1/8,  1/10 = 5 terminating decimals. 

The other 5 are not:

1,  3,  6,  7,  9 = 5 

 Nov 29, 2019
 #2
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The SMALLEST positive integer would be 6:

 

2, 4, 5 are terminating and 1, 3, 6 are not.

 Nov 29, 2019

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