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VKS comments on Rationality Quotes May 2012 - Less Wrong
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Comments (696)
3^odd = 3 mod 4
so it ends in 7.
(but I repeat myself)
I think you're mistaken. Counterexample: 3^9 = 19683.
19683 = 3 mod 4
and 3^19683 = 150 ... 859227, which ends in 7.
( The full number is 9392 digits long, which messes up the spacing in these comments. )
Oh, sorry; I agree that odd powers of three are 3 mod 4, but I had read VKS as claiming that odd powers of three had a final digit of seven; I probably misunderstood the argument. [EDIT: Yes, I was confused; I understand now.]
right, well, it's just that 3^^^3 = 3^3^3^3^3...3^3^3 = 3^(3^3^3^3...3^3^3), for a certain number of threes. So, 3^^^3 is 3^(some odd power of three).
Yes, thanks; I apologize for having misunderstood you earlier.
That is entirely ok -- I am badly in need of sleep and may have failed to optimise my messages for legibility.