It is known that 100010539 is a prime number. What is the value of
\[
{ }^{2} 4^{\wedge}\{100010538\}
\]
in modulo $100010539 ?$
a. 0
b. 13
c. 15
d. 18
e. 17
f. 1
g. 5
h. 19

Answer

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Answer

Final Answer: $\boxed{1}$

Steps

Step 1 ：Given the prime number 100010539, we need to find the value of $4^{100010538} \pmod{100010539}$.

Step 2 ：Using Fermat's Little Theorem, since 100010539 is a prime number, we have $4^{100010539-1} \equiv 1 \pmod{100010539}$.

Step 3 ：Thus, $4^{100010538} \equiv 1 \pmod{100010539}$.

Step 4 ：Final Answer: $\boxed{1}$