Linked Questions

0
votes
2answers
203 views

Discrete Mathematics help: $2017^{2017}$ mod $13$ [duplicate]

I'm not too sure how I would go about solving $2017^{2017}$ mod $13$.
1
vote
6answers
678 views

Remainder when $5^{5555}$ is divided by $10000$. [duplicate]

Find the remainder when $5^{5555}$ is divided by $10000$. A step by step guide with explanation for a beginner student in modular arithmetic is needed.
0
votes
3answers
241 views

Remainder when $333^{333}$ is divided by $7$ [duplicate]

Find the Remainder when $333^{333}$ is divided by $7$ I think I have to find $333^{333}\equiv r \pmod7$ where $r(\ge0)$ is the remainder but how do I get in that form
2
votes
2answers
823 views

Modular Arithmetic with Multiple Exponents [duplicate]

I understand how to do modular arithmetic on numbers with large exponents (like $8^{202}$). However, I am having trouble understanding how to calculate something like: $ 3^{3^{3^{3^3}}}$ mod 5 (that'...
0
votes
1answer
133 views

Find $7^{1\,000\,000\,000\,000\,000} \bmod{107}$ [duplicate]

What is a shortcut to doing this kind of problem? I know that 7 and 107 are both prime number; thus, I assume that has something to do with the appropriate approach/solution. But beyond that I am ...
2
votes
3answers
118 views

Calculation of $2^{XXXX} + 3^{XXXX}\pmod{11}$ [duplicate]

I've a question: How do I calculate $2^{2020} + 3^{2020}\pmod{11}$? Is there a theorem or any trick to do it? I need to show all the steps I used to calculate the Rest but I've no clue how to even ...
2
votes
4answers
131 views

Find $ \ \ 8^{504} \equiv \pmod 5$ [duplicate]

Find $ \ \ 8^{504} \equiv \pmod 5 $ Answer: $ 8^{504} \equiv 2^{1512} \pmod 5 $ Now , $$ \begin{align}2^4 &\equiv 1 \pmod 5 \\\text{or, } \left(2^{4}\right)^{378} &\equiv 1^{378} \pmod 5 \...
0
votes
2answers
92 views

Remainder when $4^{2018}$ is divided by $29$ [duplicate]

Find the remainder after division when $4^{2018}$ is divided by $29$. My approach: we have $$4^{2018}=16^{1009}=-\left(1-17\right)^{1009}=-\left(\binom{1009}{0}-\binom{1009}{1}17+\binom{1009}{2}17^2+...
1
vote
3answers
114 views

Detemine the unit digit of a number [duplicate]

Find the unit digit of the number: $$3^{7005} \times 6^{8000}$$ My turn: $$3^{7005}\times 6^{8000}=3^{7005}\times 3^{8000} \times2^{8000}$$ $$3^{13005} \times 2^{8000}$$ But i could not go on ?
0
votes
3answers
353 views

How to compute $21^{4600} \mod 47$ [duplicate]

I am struggling to get this problem started. I have looked at similar problems in the book I am using for class (Discrete Mathematics with Applications, 7E) but none of them are seeming to help. Any ...
0
votes
3answers
77 views

Compute $(5^{200}+7^{600}) \mod 12$ [duplicate]

Compute $(5^{200}+7^{600}) \mod 12$. I thought about somehow using the binomial theorem, but I couldn't make any progress.
1
vote
6answers
162 views

How do I find the last two digits $2012^{2013}$? [duplicate]

How do I find the last two digits 20122013 My teacher said this was simple arithmetics(I still don't see how this is simple). I thought of using Congruence equation as 2012 is congruent to 2 mod 10.....
1
vote
2answers
116 views

How to calculate mod of number with big exponent [duplicate]

I want to find $$ 5^{133} \mod 8. $$ I have noticed that $5^n \mod 8 = 5$ when $n$ is uneven and 1 otherwise, which would lead me to say that $5^{133} \mod 8 = 5$ But I don't know how to prove this. ...
2
votes
5answers
104 views

How to find remainder when $ 975^{40153}$ is divided by $14$? [duplicate]

I still find tricky this kind of problems. I tried to do solve it by factoring $14$ in $2*7$. Then, with Fermat's Little Theorem, I find that: $975^6\equiv 1\pmod 7$ $975^1\equiv 1\pmod 2$ How can ...
0
votes
1answer
441 views

How to find reminder of $m^{x}$ divided by $n$ using Euler's and Fermat's little theorem [duplicate]

How do you find reminder of $m^{x}$ divided by $n$ using Euler's and Fermat's little theorem? Can anyone show me step-by-step how to apply Fermat's little theorem and Euler's theorem? Example: What ...

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