Question

modulus of 13^2^2011 division 16
plissss plisss :(

Answer 1

what do you mean by devision 16?

Answer 2

modulus of 13^2^2011 divided by 16
plissss plisss :(

Answer 3

its zero if im right

Answer 4

you mean \[13^{2^{2011}}\] right?

If so, then you can simplify it as \[13^{4022}\] because you multiply exponents when raising an exponent to an exponent.

now find the modulus of smaller powers of 13 and see if a pattern arises

13mod(16) = 13
13^2mod(16) = 9
13^3mod(16) = 5
13^4mod(16) = 1
13^5mod(16) = 13
13^6mod(16) = 9

So there are four unique remainders for powers of 13 divided by 16 so divide the exponent by four\[4022/4 = 1005 \mod 2\]
Thus, 13^{4022} is the equivalent to 13^{2} so its remainder is 9

Answer 5

owh I'm clear now. ^_^