(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.

(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