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Nineteenth Exponent Exposition (Posted on 2016-09-06) Difficulty: 3 of 5
The number 5353714662021596247595065017236556037762353639503 is the nineteenth power of a positive integer.

Find the integer using just pen and paper.

No Solution Yet Submitted by K Sengupta    
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Some Thoughts An analytic start and a calculator finish | Comment 2 of 3 |
5353714662021596247595065017236556037762353639503

is

53537146620.21596247595065017236556037762353639503
      x 10^38
      
      
2^19 = 524288 while
3^19 = 1162261467 and
4^19 = 274877906944

so the answer is somewhere between 300 and 400.

Of course if we use a calculator we can find 19th root of 53537146620 is  3.669999999999221, in other words 3.67, so the answer would be 3.67 x 10^(38/19) = 3.67 x 10^2 = 367.


  Posted by Charlie on 2016-09-06 15:42:04
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