COMEDK · Maths · 1. Basic of Mathematics
If \(49^{n}+16 n+P\) is divisible by 64 for all \(n \in N\), then the least negative integral value of \(P\) is
- A \(-2\)
- B \(-3\)
- C \(-4\)
- D \(-1\)
Answer & Solution
Correct Answer
(D) \(-1\)
Step-by-step Solution
Detailed explanation
Let \(f(n) = 49^{n} + 16n + P\). We are given that \(f(n)\) is divisible by 64 for all \(n \in N\). For \(n = 1\), \(f(1) = 49^{1} + 16(1) + P = 49 + 16 + P = 65 + P\). For \(f(1)\) to be divisible by 64, \(65 + P = 64k\) for some integer \(k\). For \(n = 2\),…
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