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in Mathematical Induction by (48.8k points)
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If xn – 1 is divisible by x – k, then the least positive integral value of k is

A. 1
B. 2
C. 3
D. 4

1 Answer

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Best answer

A. 1

Given; P(n): xn – 1 is divisible by x – k

⇒ P(1) : x – 1

⇒ P(2) : x2 – 1 = (x−1)(x+1)

⇒ P(3) : x3 – 1 = (x−1)(x2+xy+1)

⇒ P(4) : x4 − 1 = (x2−1)(x2+1) = (x−1)(x+1)(x2+1)

∴ The least positive integral value of k is 1.

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