Question 1204411
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Hint: When dividing by 9, the remainder is equal to the sum of the digits.


Examples:
14/9 = 1 remainder 5, and 1+4 = 5
28/9 = 3 remainder 1, and 2+8 = 10 --> 1+0 = 1
45/9 = 5 remainder 0, and 4+5 = 9, getting remainder 9 is the same as remainder 0
127/9 = 14 remainder 1, and 1+2+7 = 10 --> 1+0 = 1


Notice how for some large sums, we have to add the digits up again. 
This process is carried out until landing on a digit sum that is between 1 and 9.
If the digit sum is 9, then the original number is a multiple of 9.
This divisibility rule is very similar to the divisibility by 3 rule.



Another hint:
2+7+4+5+6+3+3+5+8 = 43 ---> 4+3 = 7
Therefore, 274563358/9 = some quotient remainder 7
We can then rephrase the problem as asking: What is the remainder of 7^5 when divided by 9?


One final hint: The powers of 7 mod 9 repeat themselves every three terms.
In other words,
7^1 = a (mod 9)
7^2 = b (mod 9)
7^3 = c (mod 9)
7^4 = a (mod 9)
and so on
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