Question

5.

(a) Find the values of 2^{k} mod 9 where k = 1, 2, 3, 4, 5,
6, 7, 8, 9.

(b) Find the remainder of 2^{271} when this number is
divided by 9.

(c) Find the remainder of 2^{271} when this number is
divided by 5.

PLEASE GIVE RIGHT ANSWERS AND GOOD DETAILS ON HOW TO GET THE ANSWERS

THE ANSWERS I GOT YESTERDAY FROM YOUR GUYS WERE WRONG!!!

Answer #1

5)a) If k=1,then 2k=2 and then if we divide it by 9 ,we get the remainder 2. Therefore 2k(mod9)=2,when k=1.

Similarly if k=2, then 2k=4,then if we divide it by 9,we get the remainder 4,Therefore 2k(mod9)=4.

Similarly 2k(mod9)=6,for k=3 and 2k(mod 9)=8,for k=4.

If k=5,then 2k=10,then if we divide it by 9,we get the remainder 1,Therefore 2k(mod9)=1,for k=5.

Similarly 2k(mod 9)=3,5,7,0 for k=6,7,8,9 respectively.

5.b)We have 2271=252×9+3.then if we divide 2271 by 9,we get the remainder 3.

5.c)We have 2271=454×5+1,then if we divide it by 9,we get the remainder 1.

Find all solutions to the system:
2x ≡ 4 (mod 5)
3x ≡ 5 (mod 7)
7x ≡ 2 (mod 13)
need help with discrete math HW, please write solutions clearly,
and please don't just answer wrong solution, cus then i will need
to post the same question twice. i appreciate every help i can get
but please let someone else help me solve the question if you're
not sure about any part to avoid reposting. thanks, will rate best...

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x ≡ 5 (mod 5)
x ≡ 3 (mod 7)
x ≡ 8 (mod 11)
x ≡ 2 (mod 17)
need help with discrete math HW, please write solutions clearly,
and please don't just answer wrong solution, cus then i will need
to post the same question twice. i appreciate every help i can get
but please let someone else help me solve the question if you're
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x = 2 (mod 3)
x = 4 (mod 5)
x = 5 (mod 8)
I have the answer the professor gave me, but I can`t understand
what`s going on. So if you could please go over the answer and
explain, it would help a lot.
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x = 3a + 2
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H
C
O
F
3 , 7
9 , 13
12 , 16
M
1 , 5
3, 7
2, 6
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answer if 3.5 but I don't know how to get there. I found the Sum of
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Number
-5
6
8
-2
6
9
8
2
1
6
2
1
Find the following :
Mean
Standard Error
Median
Mode
Standard Deviation
Sample Variance
Kurtosis
Skewness
Range
Minimum
Maximum
Sum
Count
Confidence Level(95.0%)
Give three decimals for all answers.
Please make sure that the meaning of three decimals is
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i
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