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1. Postive integer...
is the correct answer...
Answer:
Option(3)
Step-by-step explanation:
Let the given statement be P(n). Then,
P(n) = (xⁿ + aⁿ) is divisible by x + a.
When n = 1:
LHS : x¹ + a¹ = x + a
RHS : x + a
Thus, the given statement is true for n = 1, i.e P(1) is true.
Let P(2k + 1) is true. Then,
P(2k + 1) : x^(2k + 1) + a^(2k + 1) is divisible by (x + a).
Now,
Thus, P(1) is true and P(k + 1) is true, whenever P(k) is true.
Hence,by the mathematical induction, P(n) is true for all odd positive integer.
Hope it helps!