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

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The discussion centers on proving whether the numbers 2^((n-2)/2) - 1 and 2^(2n) + 1 are relatively prime. It is established that for odd values of n, the first expression does not yield an integer. Specifically, when n=18, the first number evaluates to 255 and the second to 2^36 + 1, both of which are divisible by 17, confirming that the two numbers are not relatively prime for all values of n.

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Naveenks
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Hi, Can anyone help me how to prove that the two numbers 2^((n-2)/2) -1, 2^(2n) + 1 are relatively prime?
Thanks.
 
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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.
 
Thanks Dodo...I got it that the two numbers are not relatively prime for all values of n...
 

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