Can someone please explain this problem.
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Module 5 Day 3 Your Turn Part 3 Mini-Question Solution
It says that this number is odd, when it is even because 8^7^6^5 and so on can be expressed as 8^(7!), and we know that even*even=even.
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Very close! It would only be equal to 8^(7!) if there were parentheses around each term like this:
If there are no parentheses, the powers cannot be multiplied, and so it equals this:
Since the exponent on the 8 is a power of 7, which is odd, the answer is equal to 8^{1} mod 9. -
@v4913 said in Can someone please explain this problem.:
Very close! It would only be equal to 8^(7!) if there were parentheses around each term like this:
If there are no parentheses, the powers cannot be multiplied, and so it equals this:
Since the exponent on the 8 is a power of 7, which is odd, the answer is equal to 8^{1} mod 9.o pro v4913 post o
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@v4913 Ok, thanks! I also have another question about this problem. When it is odd, why is the answer -1 mod 9?
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@neatlobster @v4913 Thank you
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@neatlobster Good question! Since 8 = -1 mod 9, and the powers of -1 go -1, 1, -1, 1, etc, all (-1)^{even} = 1 mod 9 and all (-1)^{odd} = -1 mod 9. Since we are talking about modulos, and 8 is the same as -1 mod 9, this means (8)^{even} = 1 mod 9, and (8)^{odd} = -1 mod 9.
