Recent content by scottyk

add the two "towers" of exponents thats is 5^... + 10^...

Here is how i plan to write up the problem: We notice that powers of 10 (mod 11) form a pattern: 10^0 mod 11 = 1 10^1 mod 11 = 10 10^2 mod 11 = 1 10^3 mod 11 = 10 . . . So all the odd powers of 10 are equal to 10 (mod 11). Clearly, the exponent of the first term is odd: it's some...

Ok, so let's take it one step further: would 10^5^10^5^10 + 5^10^5^10^5 be divisble by 11? i know that each tower is not divisble by 11, but what about when you add them together? i'm not sure why this is confusing me so much...maybe I'm making it too complicated?

but is there a way to break down the "tower" into a smaller integer using modulo 11? i know that indeed this integer is not divisible by 11, but many students are confused by the tower. For example, 21 is equivalent to -2 for mod 23. Is there a way to find that 5^10^5^10^5 is equivalent...

I'm really stuck on the following problem: I'm trying to determine whether or not 5^10^5^10^5 is divisible by 11... i have tried a few different methods and can't figure this out. I know the trick must have something to do with modulo 11, but I am not sure exactly how to get the...