KCET · Maths · Binomial Theorem
The remainder obtained when \(5^{124}\) is divided by 124 is
- A 5
- B 0
- C 2
- D 1
Answer & Solution
Correct Answer
(A) 5
Step-by-step Solution
Detailed explanation
We have, \(5^{124}=\left(5^{3}\right)^{41} \cdot 5\)
Now, \(\quad 5^{3}=1(\bmod 124)\)
\(\therefore \quad\left(5^{3}\right)^{41}=1(\bmod 124)\)
\(\left(5^{3}\right)^{41} \cdot 5=1 \cdot 5(\bmod 124)\)
\(\Rightarrow \quad 5^{124}=5(\bmod 124)\)
Now, \(\quad 5^{3}=1(\bmod 124)\)
\(\therefore \quad\left(5^{3}\right)^{41}=1(\bmod 124)\)
\(\left(5^{3}\right)^{41} \cdot 5=1 \cdot 5(\bmod 124)\)
\(\Rightarrow \quad 5^{124}=5(\bmod 124)\)
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