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| Math Central | Quandaries & Queries |
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Question from Tom, a student: Last year (2007) in a school math test we got this: Prove that there's a unique positive integer of 2007 digits length, divisible by 2^2007, and made up solely by the digits 2 and 5. No one could solve it. Please can you help us? |
Hi Tom,
Are you sure the problem wasn't
Prove that there's a unique positive integer of 2007 digits length, divisible by 2^2007, and its only prime factors are 2 and 5.
If this is the problem then one number with 2007 digits is 1 followed by 2006 zeros, that is 1 × 102006. But 10 = 2 × 5 so 102006 = (2 × 5)2006 = 22006 × 52006.
Does this help?
Penny
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