Calculate 3^274 With fermats little theorem

To calculate \(3^{274} \mod n\) using Fermat's Little Theorem, we need to know that this theorem applies when \(n\) is a prime number. The theorem states:

\[
a^{p-1} \equiv 1 \ (\text{mod} \ p)
\]

for any integer \(a\) where \(p\) is a prime number and \(a\) is not divisible by \(p\).

For the calculation of \(3^{274} \mod n\), you need to specify \(n\). If \(n\) is prime, Fermat's Little Theorem can be applied directly.

Let me know if you have a specific prime number in mind or if you need further help!

Learn how to calculate 3 raised to the power of 274 using Fermat's Little Theorem in modular arithmetic. Understand the theorem's application for prime numbers and its implications. Suitable for advanced high school students and those interested in number theory.

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