Answered

Westonci.ca connects you with experts who provide insightful answers to your questions. Join us today and start learning! Explore comprehensive solutions to your questions from a wide range of professionals on our user-friendly platform. Get quick and reliable solutions to your questions from a community of experienced experts on our platform.

For which other positive integers a, less than 11, will the number (a^n) + (a^n+1) + (a^n+2) + (a^n+3) + (a^n+4) always be divisible?
Pls, Answer with the entire explanation.

Sagot :

LammettHash

If the number is supposed to be

[tex]a^n + a^{n+1} + a^{n+2} + a^{n+3} + a^{n+4}[/tex]

then it can be factorized as

[tex]a^n \left(1 + a + a^2 + a^3 + a^4\right)[/tex]

but there's not much to say about divisibility here without any more information about a.

If you meant

[tex]a^n + (a^n+1) + (a^n+2) + (a^n+3) + (a^n+4)[/tex]

simplifying gives

[tex]5a^n + 10 = 5 (a^n+2)[/tex]

which is clearly divisible by 5.

We appreciate your visit. Our platform is always here to offer accurate and reliable answers. Return anytime. Thank you for visiting. Our goal is to provide the most accurate answers for all your informational needs. Come back soon. We're here to help at Westonci.ca. Keep visiting for the best answers to your questions.