When P is a natural number- then P n -1- P -12 n -1 is divisible by A- PB- P 2- PC- P 2- P -1D- P 2-1

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nCr Definitions and Properties

When P is a n...

Question

When P is a natural number, then $P^{n + 1} + (P + 1)^{2 n - 1}$ is divisible by

P

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P^{2} + P

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P^{2} + P + 1

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P^{2} + 1

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Solution

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p^{n + 1} + (p + 1)^{2 n - 1}

p^{2}

I + p + p^{2} + . . . . . . + p^{n} = 0

p^{- 1}

f_{p} (β) = (cos \frac{β}{p^{2}} + i sin \frac{β}{p^{2}}) + (cos \frac{2 β}{p^{2}} + i sin \frac{2 β}{p^{2}}) \dots \dots (cos \frac{β (p - 1)}{p^{2}} + i sin \frac{β (p - 1)}{p^{2}}) + (cos \frac{β}{p} + i sin \frac{β}{p})

lim n \to \infty 1 / f_{n} (π) =

I + p + p^{2} + . . . . . + p^{n} = 0

p^{- 1}

p² - 1 =

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