wsldam
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Prove that 3n + 1 has an odd prime divisor for all natural numbers > 1. I tried using order but it didn't really get me anywhere. Would prefer hints rather than complete solutions. Thanks.
3^n+1 has an odd prime divisor
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If you can't see how to prove this sort of result, start by playing around with the numbers.
Work out the values of a few numbers, 32+1, 33+1, 34+1, ... What do you notice about them?
Work out the values of a few numbers, 32+1, 33+1, 34+1, ... What do you notice about them?
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welcome to pf!
hi wsldam! welcome to pf!
isn't that another way of saying that 2m can never be of the form 3n + 1 ?
hi wsldam! welcome to pf!
wsldam said:
isn't that another way of saying that 2m can never be of the form 3n + 1 ?
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tiny-tim said:hi wsldam! welcome to pf!
isn't that another way of saying that 2m can never be of the form 3n + 1 ?
It is also saying that 3n + 1 is never an odd prime (but that's easy to show).
Norwegian
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solution 1: Do it modulo 8
solution 2: Do it for m odd (mod 3) and m even (factor 2m-1).
solution 2: Do it for m odd (mod 3) and m even (factor 2m-1).
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nice!