Through some miscellaneous reading I have stumbled upon Graham's number and more precisely, a method of calculating the $d$ rightmost digits of the number. The exact method of calculation seems straightforward through modular exponentiation. However, there is the claim that all power towers of height at least $d + 2$ will have their $d$ rightmost digits constant and independent of the topmost term of the tower. (At the risk of being too verbose, I redirect you to the Wikipedia article on Graham's number, bottom section.) I was wondering if anyone can provide a proof for the given statement.
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That passage in wikipedia is referenced, and the reference includes a discussion on why that's true. |
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