Problems & Puzzles: Puzzles Puzzle 188. Dividing large numbers Now a very simple task:
Solution: Ken Wilke, Jim Howell and Flavio Torasso found  each one by his own side  the solution asked:
Each one discovered by their own that solving this puzzle needs not  by any means  a big numbers package software, but only a very small and simple code to emulate the basic algorithm of the division "by hand". The basic feature of this algorithm is that you need not consider the number S in all his extension but only one digit at a time  form left to right  that you will concatenate to the residue of the previous step, etc... The three solvers also found several other K values larger than 8,468,396 such that S is again divided by 692399. In particular Jim found the first instance where K is also a prime number: K = 21830773, having S 163,535,081 digits for this K value. *** As a curios note I would like to add that if we relax the condition of taking all the digits of the final K number to just taking some of the first digits of it, then the smallest solution is this one:
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