Just for fun!-XVII
Number Theory
Level
3
Let be the least positive integer divisible by 17 whose digits sum to 17. Find .
The answer is 476.
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1 solution
The digit sum of a base 10 integer m is just m . In this problem, we know 17 m, or m=17k for a positive integer k.
Also, we know that m = 17 = -1 or 17k = -k = -1 Obviously k=1 is a solution. This means in general, k=9x+1 is a solution for non-negative integer x.
Checking the first few possible solutions, we find that m=476 is the first solution that has s(m)=17, and we're done. :)