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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 $\displaystyle 29$

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).

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. 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?

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.


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