Linked Questions

1
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1answer
77 views

Fermats little theorem, $p$ is not a prime number [closed]

Calculate the remainder $$ r \equiv 37^{877} \bmod{323} $$ I don't know how to follow this up since $323$ is not a prime number.
0
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4answers
111 views

Least positive integer $\equiv 3^{18} \pmod{37}?$

To determine this for $13^{33} \pmod{64}$ is easy since $\phi(64)=32$ and $\gcd(64,33)=1$, we have $13^{\phi(64)}=13^{32}\equiv1 \pmod{64}$. This means that $$13^{33}=13^{31}\cdot13\equiv 13 \equiv1 \...
0
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4answers
65 views

Check if an expression is divisible by 2016. (modulo operations?)

How to check whether $29^{576} - 1$ can be divided by $2016$ without computing the numbers? I suppose that I have to use modular arithmetic, but don't really know how...
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votes
1answer
106 views

How can I reduce this $3456^7 \cdot 3456^7 \pmod{2099}$? [closed]

The original form was $3456^{14} \pmod{2099}$, but now I need to break down the 3456 so that I may perform the modulo operation
0
votes
2answers
80 views

Remainder when $3^{12} + 4^{21}$ is divided by 13.

What is remainder when $3^{12} + 4^{21}$ Is divided by 13? I tried this question by found binomial theorem but as there are two bases it is becoming difficult to calculate . I am a school going ...
0
votes
1answer
44 views

How to find the last digit of a number in base b?

For a number $a^{x^{...^n}} $. To find its last digit in a base b, Imagine that I have this number $a^{x^{y}}$ to simplify the problem. Then I calculate $a^{x} \equiv c \pmod b$ and after that $c^{...
0
votes
1answer
88 views

calculate modular algorithm with large exponents [duplicate]

I don't know how to calculate the following modulo: $$321^{654} \mod 1013$$ Are there some easy way to do this?
0
votes
0answers
85 views

How to compute a big number modulo x? [duplicate]

I still have problems computing (without a calculator) for example: $R_{21}(3^{234})$ I know i have to use the chinese reminder theorem, bu before that, how do i get there? I know that i haw to split ...
1
vote
2answers
58 views

Easy Number Theory modular exponentiation

So I was reading through some old questions I found For the question I was asked to explain why for $\,2018^{\large 2017^{\LARGE n}}\!\!\bmod 1001$ Where n is an integer between 14 million and 17 ...
-1
votes
3answers
70 views

What will be the remainder if $7^{101}$ mod $5$? [closed]

$$7^{101} \mod 5 = 49^{100} \mod 5 = (49^2)^{50} \mod 5$$ What is the next step to find solution? Regards
1
vote
4answers
34 views

Large Remainders with Mod

Determine the remainder of $5^{2017}$ when divided by 7. I know that we need to use mod 7 to find all of the different remainders but I am not sure what specific steps to take and how to finish it ...
0
votes
2answers
33 views

Congruence with powers

How would one go about solving the following congruence: $x\equiv2^{2012} \pmod6$ I assume you can divide that number on the left to lower it, but how exactly? Same issue applies to $x\equiv6^{29} \...
1
vote
1answer
53 views

Solving the equation for x

I need help solving for $x$ on the following congruence $x^{49943} \equiv 10855$ mod ($63571$). I started computing $\phi (63571) = 63000$, where $\phi$ is the Euler Phi function. Next, we solve ...
0
votes
2answers
36 views

Modulus algorithm for finding a*b^c mod n, avoiding large numbers?

I know the algorithm finding $ (a^b) mod\;n $ avoiding large numbers so I can code it, but I'm wondering if anyone can help me with a similar algorithm for $$ (a\cdot b^c )mod\;n $$ It's quite hard ...
0
votes
5answers
68 views

Modular equation with exponents on the exponents

I want to solve this modular equation: $ 7x + 5 \equiv 2^{11^{2017}} \pmod {31}$ As far as I know, dividing the exponent by 31 and substituting it with the remainder is not allowed. I've looked ...

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