Determine the minimum value of a positive integer N > 2 such that:
the number 199...991, containing precisely N nines, is divisible by 1991.

N=180   Aided by Excel only.

edited : I have erroneously started with  N(0)=1991,

and continued : h(K)=mod(N(K),1991)

N(K)= MOD(10*h(K-1)+81),1991

So the value 0 is reached when  N=182 (corrected answer).

Edited on January 29, 2016, 3:44 pm

Posted by Ady TZIDON on 2016-01-29 09:24:59