Are 2^((n-2)/2) - 1 and 2^(2n) + 1 Relatively Prime?

[Naveenks]

Hi, Can anyone help me how to prove that the two numbers 2^((n-2)/2) -1, 2^(2n) + 1 are relatively prime?
Thanks.

 

[dodo]

Hi, Naveenks,
check the question again; if n is odd, the first number is not an integer.

Besides, when n=18, the first number would be 2^8-1 = 255, and the second 2^36+1, and both are divisible by 17.

 

[Naveenks]

Thanks Dodo...I got it that the two numbers are not relatively prime for all values of n...