My Math Forum sum of digit is equal to 29

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 May 30th, 2016, 08:15 PM #1 Senior Member   Joined: Jul 2011 Posts: 405 Thanks: 16 sum of digit is equal to 29 How many $\displaystyle 4$ digit numbers divisible by $\displaystyle 29$ have the sum of digit is $\displaystyle 29$ Thanks from manus
 May 30th, 2016, 11:30 PM #2 Global Moderator   Joined: Dec 2006 Posts: 20,747 Thanks: 2133 There are five (4988, 7598, 7859, 9686 and 9947). Thanks from panky
 May 31st, 2016, 07:58 AM #3 Senior Member   Joined: Dec 2015 From: somewhere Posts: 536 Thanks: 81 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. Thanks from manus Last edited by skipjack; May 31st, 2016 at 08:22 AM.
 May 31st, 2016, 08:21 AM #4 Global Moderator   Joined: Dec 2006 Posts: 20,747 Thanks: 2133 Use what series and how? Thanks from manus
 May 31st, 2016, 06:53 PM #5 Senior Member   Joined: Jul 2011 Posts: 405 Thanks: 16 Thanks moderator, would you like to explain me how can we get it. Thanks from manus

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### possible 4 digit equal 29

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