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Ninety Seven and Divisibility Nuance (Posted on 2021-12-12) Difficulty: 2 of 5
Determine the minimum value of a positive integer N such that:
o N has the form: 97.......97, and:
o N is divisible by 99

No Solution Yet Submitted by K Sengupta    
Rating: 4.0000 (1 votes)

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re(2): solution | Comment 3 of 10 |
(In reply to re: solution by K Sengupta)

I had been under the impression that N would consist solely of repetitions of 97.


However, if the ellipsis dots can be any values, the lowest 10 values that work are

     9712197
     9722097
     9731997
     9741897
     9751797
     9761697
     9771597
     9781497
     9791397
    97109397

much lower than  9731999999997

found by

a=9700; chk=9800; ct=0
for b=97:100:40000000097
   if a+b>=chk
      a=10*a;
      chk=10*chk;
   end
   if mod(a+b,99)==0
      disp(a+b) 
      ct=ct+1;
      if ct>=10
         break 
      end
   end
end


  Posted by Charlie on 2021-12-12 15:19:21
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