COMEDK · Maths · 7. Binomial Theorem
The remainder when \(7^{103}\) is divided by \(25\) is
- A \(7\)
- B \(18\)
- C \(1\)
- D \(-1\)
Answer & Solution
Correct Answer
(B) \(18\)
Step-by-step Solution
Detailed explanation
We need to find the remainder when \(7^{103}\) is divided by \(25\). We can write \(7^{103}\) as \(7 \cdot 7^{102} = 7 \cdot (7^2)^{51}\). We know that \(7^2 = 49 \equiv -1 \pmod{25}\). Raising both sides to the power of \(51\), we get: \((7^2)^{51} \equiv (-1)^{51} \pmod{25}\)…
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