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Proper Power Poser (Posted on 2015-05-23) Difficulty: 3 of 5
Without direct evaluation, determine whether 1021991 + 1031991 is a proper power of an integer.

No Solution Yet Submitted by K Sengupta    
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Possible solution. Comment 1 of 1

1021991 + 1031991 = 205*(a mess)

205 = 5*41

Last digits of small odd values of a mess for 102(2n-1) + 103(2n-1)(even ones are fractional):

{1,7,5,3,9,9,3,5,7,1,1..}

5 divides a mess iff 5 divides (2n-1)

5 does not divide 1991.

Therefore 1021991 + 1031991  is not a proper power of an integer.


Edited on May 24, 2015, 4:10 am
  Posted by broll on 2015-05-24 03:49:02

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