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Prime and power poser (Posted on 2011-10-09) Difficulty: 2 of 5
(i) Determine all possible prime(s) M such that 2*M + 1 is a perfect cube.

(II) Determine all possible prime(s) M such that 16*M + 1 is a perfect fourth power.

No Solution Yet Submitted by K Sengupta    
Rating: 3.0000 (2 votes)

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Solution re: possible answer | Comment 2 of 3 |
(In reply to possible answer by Dej Mar)

 

D1  at  most

No need to test 1000 numbers, just "reverse reasoning":

   i  3 is the only odd prime not of the 6k+1 or 6k-1  type., Those cubed -1 and divided by 2 cannot be prime

ii  similar reasoning

Edited on October 9, 2011, 3:38 pm
  Posted by Ady TZIDON on 2011-10-09 15:28:56

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