The 2 has nothing to do with it. The 25 happens because in obtaining the next higher square you do 5 * (current value). Since the current value ends in 5 and 5 * 5 = 25, you will end in 25. similarly, in base 8 when using 4 (the middle value, like 5 is in base 10) all answers end in 0. (4 * 4 = 10, 4 * 10 = 40, ...) The main thing is that we use a nonprime counting method. In any nonprime system there will exist some number n, where n = (length of system / 2) that when multiplied by itself any number of times will give you the same last digit. As for last 2 digits, that might have to do with the (5 * 2). I'll have to see if it holds up in other systems with only two factors
Yep, at least in systems with 2 prime factors where one is 2 it holds true. now to try the fun decimal multiplication in systems that are not base10...
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The integral z squared dz
From one to the square root of three
Times the cosine
Of three pi over nine
is the log of the cube root of e!
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