It is known that 100010539 is a prime number. What is the value of
\[
94^{100010538}
\]
in modulo $100010539 ?$
a. 0
b. 13
c. 15
d. 18
e. 17
f. 1
g. 5
h. 19
Answer
Calculating the value of \(94^1 \pmod{100010539}\), we get \(\boxed{94}\) as the final answer.
Step 1 ：Given that 100010539 is a prime number, we want to find the value of \(94^{100010538}\) in modulo 100010539.
Step 2 ：Using Fermat's Little Theorem, which states that if p is a prime number, then for any integer a, \(a^p \equiv a\) (mod p), we can rewrite the expression as \(94^{100010539-1} \pmod{100010539}\).
Step 3 ：According to Fermat's Little Theorem, this is equivalent to \(94^1 \pmod{100010539}\).
Step 4 ：Calculating the value of \(94^1 \pmod{100010539}\), we get \(\boxed{94}\) as the final answer.
