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How many Integers? (Posted on 2006-05-18) Difficulty: 2 of 5
Find the number of positive integers that divide (10)^999 but not (10)^998.

No Solution Yet Submitted by Ravi Raja    
Rating: 3.0000 (1 votes)

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Solution Quick | Comment 4 of 9 |
10^999=2^999x5^999, so it has (999+1)x(999+1) = 1000^2 divisors. Similarly, 10^998 has 999^2 divisors. The difference is 1000^2-999^2= (1000+999)(1000-999)= 1999.

  Posted by Federico Kereki on 2006-05-18 10:00:58
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