Thread: is it possible
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Old 2020-07-14, 08:13   #12
JeppeSN
 
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"Jeppe"
Jan 2016
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Quote:
Originally Posted by drmurat View Post
I asked it because if 2^(n) + 1 is prime and 2^(n+1) + 1 can be prime . it means
(2^n) * (2^ (2n) + 1) *(2^ (2n+1) + 1)
gives perfect number
but it is impossible . one of them is devided by 3
It is true that one of them is divisible by 3. Modulo 3, we have 2^n + 1 ≡ (-1)^n + 1, so every second n produces zero modulo 3.

As mentioned above, n=0 and n=1 both work, because 2^0+1; 2^1+1; 2^2+1 gives 2; 3; 5. For n=0 your formula does make a perfect number, but for n=1, the way I read it, your formula gives 90, which is not perfect.

/JeppeSN
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