Problem
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
Solution
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: \(\boxed{1}\)
