Question

If p be a positive integer then prove by the principal of Induction that p^n+1+(p+1)^2n-1 is divisible by p^2+p+1 for all n=Natural numbers

Answer 1

Answer:

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Step-by-step explanation:

Let P(n) : Pn + 1 + (p + 1)2n - 1 is divisible by p2 + p + 1. For n = 1, P(1): p2 +(p+1)1 which is divisible by p2 + p + 1 .'. P (1)is true. Let P (k) be true. ie, .'. P (k+ 1) is divisibleby p2 + p + 1 .'. P (k + 1) is true. Hence, by mathematical induction P (n) is true for all n ∈ N.Read more on Sarthaks.com - https://www.sarthaks.com/287609/if-p-be-natural-number-then-prove-that-1-p-1-2n-1-is-divisible-by-p-2-for-every-positive-integer

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