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May 30th, 2016, 08:15 PM   #1
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sum of digit is equal to 29

How many $\displaystyle 4$ digit numbers divisible by $\displaystyle 29$ have the sum of digit is $\displaystyle 29$
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May 30th, 2016, 11:30 PM   #2
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There are five (4988, 7598, 7859, 9686 and 9947).
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May 31st, 2016, 07:58 AM   #3
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First find interval of$\displaystyle \;$ $\displaystyle K$ where $\displaystyle 29K$ has 4 digits, and $\displaystyle K \;$ is a natural number
$\displaystyle 3=[\log29K]$
Number of digits of an integer $\displaystyle N$ equals $\displaystyle 1+[\log{N}]$
4 = 1 + log[29K]; for sum of digits, use series.
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Last edited by skipjack; May 31st, 2016 at 08:22 AM.
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May 31st, 2016, 08:21 AM   #4
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Use what series and how?
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May 31st, 2016, 06:53 PM   #5
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Thanks moderator, would you like to explain me how can we get it.
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