Let denote the sum of the digits of the positive integer in decimal notation. What may be if and ?

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- Dec 15th 2007, 03:32 AM #1

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- Dec 15th 2007, 04:35 AM #2

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Hello, james_bond!

Is this a trick question?

Let denote the sum of the digits of the positive integer in decimal notation.

What may be if and ?

Anyone familiar with "Casting out 9's" know this fact . . .

. . If is the digital-sum function: .

(Hmm, that's not quite accurate, but it'll do.)

If , then: . .*. . . too easy*

- Dec 15th 2007, 05:20 AM #3

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- Dec 21st 2007, 07:07 PM #4
I know.

*a*is the 100-digit number consisting of all 1’s, so 124*a*is the 102-digit number whose first two digits are 13 and last two 64, with 98 7’s in between. Hence f(3*a*) = 300 after all.

- Dec 22nd 2007, 05:42 AM #5

- Dec 22nd 2007, 06:30 AM #6