A) 5
B) 0
C) 2
D) 1
Correct Answer: A
Solution :
We have, \[{{5}^{124}}={{({{5}^{3}})}^{41}}\cdot 5\] Now, \[{{5}^{3}}=1(\bmod \,\,124)\] \[\therefore \] \[{{({{5}^{3}})}^{41}}=1(\bmod \,\,124)\] \[{{({{5}^{3}})}^{41}}\cdot 5=1\cdot 5(\bmod \,\,124)\] \[\Rightarrow \] \[{{5}^{124}}=5(\bmod \,\,124)\]
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