# Solution to previous Problem of the Week

*What is the remainder when f(x)=999x^{999}+998x^{998}+997x^{997}+. . .+2x^{2}+x is divided by x-1?*

This is a finite polynomial of degree 999. For us to solve this problem we need to know that f(a) is the remainder when f(x) is divided by x-a. That is the famous remainder theorem.

The remainder when* f(x)=999x^{999}+998x^{998}+997x^{997}+. . .+2x^{2}+x* is divided by

**is also**

*x-1**.*

**f(1)****f(1)= 999(1) ^{999}+998(1)^{998}+997(1)^{997}+. . .+2(1)^{2}+(1)**

**f(1)= 999+998+997+. . . +2+1**

Using the formula for the sum of arithmetic series we have,

where * a_{1}* and

**are the first and last term respectively,**

*a*_{n}*is the number of terms.*

**n***f(1)=999(1+999)/2*

*f(1)=499500*

Here is the link to that page

### Dan

#### Latest posts by Dan (see all)

- 2016 MMC Schedule - November 4, 2015
- 2014 MTAP reviewer for Grade 3 - September 30, 2015
- 2015 MTAP reviewer for 4th year solution part 1 - August 22, 2015

prove the following.in THEORY OF EQUATION

1. If R; +,∙ ›is a ring , then for any a Є R,0 ∙a = a ∙0=0, where 0 is the additive identity.

2. Let R be an abelian ring, then Øc : R[x]→R such that Øc(p(x)) = p(c) is a ring homomorphism

Can you help me to answer this question.Thank you

fy8VnE J aapprecie cette photo mais j aen ai auparavant vu de semblable de meilleures qualifications;

It as nearly impossible to find well-informed people for this topic, however, you sound like you know what you are talking about! Thanks

This is one awesome article post. Fantastic.

I think other web site proprietors should take this web site as an model, very clean and great user genial style and design, let alone the content. You are an expert in this topic!

Muchos Gracias for your article.Much thanks again. Keep writing.

This post is indeed quite interesting. Keep it up! I all try here to further the contributions Vervolg.

Great, thanks for sharing this blog.Really thank you! Will read on…

There is definately a great deal to find out about this subject. I love all of the points you made.

I really liked your article post.Much thanks again. Cool.

Im thankful for the article.Much thanks again. Awesome.

whoah this blog is excellent i love reading your posts. Keep up the great work! You know, a lot of people are searching around for this info, you could aid them greatly.

You ave got some true insight. Why not hold some sort of contest for the readers?

Im no pro, but I suppose you just made an excellent point. You naturally understand what youre talking about, and I can truly get behind that. Thanks for being so upfront and so honest.

Im obliged for the blog article. Really Cool.

This is very interesting, You are a very skilled blogger. I have joined your rss feed and look forward to seeking more of your great post. Also, I ave shared your web site in my social networks!

Thanks so much for the article.Really looking forward to read more. Keep writing.

Usually I do not read post on blogs, but I wish to say that this write-up very pressured me to try and do it! Your writing taste has been amazed me. Thanks, very nice post.

There is clearly a bundle to know about this. I assume you made certain nice points in features also.

Thanks for the blog.Really looking forward to read more. Really Great.

This unique blog is obviously interesting and also diverting. I have picked up many handy things out of it. I ad love to go back over and over again. Cheers!

You should participate in a contest for the most effective blogs on the web. I will suggest this web site!

Im grateful for the blog post.Really looking forward to read more. Really Cool.

Major thanks for the blog post.Much thanks again. Awesome.

Muchos Gracias for your article. Awesome.

Thanks for sharing, this is a fantastic blog.Really thank you! Fantastic.

When I look at your blog in Safari, it looks fine but when opening in Internet Explorer, it

Thanks so much for the article post.Really looking forward to read more. Great.

I really enjoy the post.Thanks Again. Keep writing.

Muchos Gracias for your article post.Thanks Again. Will read on

This awesome blog is definitely interesting additionally diverting. I have found a bunch of interesting things out of it. I ad love to return over and over again. Cheers!

Thanks so much for the article post.Really looking forward to read more. Much obliged.

I loved your article.Much thanks again. Fantastic.

A round of applause for your article.Thanks Again. Will read on…

I went over this website and I believe you have a lot of fantastic info, bookmarked (:.

Wow, great blog.Really thank you! Great.

I really liked your blog post. Will read on

Major thankies for the post.Really looking forward to read more. Great.

Very good article. Want more.

Wow! This can be one particular of the most beneficial blogs We have ever arrive across on this subject. Actually Great. I am also a specialist in this topic so I can understand your effort.

Really informative blog.Really thank you! Awesome.

I truly appreciate this blog.Thanks Again. Awesome.

Quite Right I definitely liked the article which I ran into.

You completed a number of fine points there. I did a search on the topic and found mainly persons will go along with with your blog.

It as hard to find experienced people on this subject, however, you seem like you know what you are talking about! Thanks

There is perceptibly a bundle to identify about this. I believe you made various good points in features also.

Its hard to find good help I am regularly saying that its difficult to get quality help, but here is

Very nice write-up. I definitely appreciate this site. Thanks!

Many thanks! It a wonderful internet site!|

Wow, incredible blog layout! How long have you been blogging for? you made blogging look easy. The overall look of your site is great, let alone the content!. Thanks For Your article about sex.

Thanks for sharing, this is a fantastic blog.Much thanks again. Want more.

Im thankful for the post.Thanks Again. Much obliged.

Thanks again for the blog.Really looking forward to read more. Fantastic.

Some genuinely nice and utilitarian info on this website , besides I think the design and style contains fantastic features.

I loved your blog article.Really thank you! Will read on…

Major thankies for the post.Really looking forward to read more.

Regards for this tremendous post, I am glad I detected this internet site on yahoo.

I value the article post.Much thanks again. Awesome.

Your style is so unique compared to other people I have read stuff from. Thank you for posting when you ave got the opportunity, Guess I all just book mark this site.

Major thankies for the post.Thanks Again. Great.

please stop by the sites we follow, such as this a single, because it represents our picks in the web

Thanks for the blog article.Thanks Again. Cool.

Im obliged for the blog post.Really thank you! Great.

Thanks-a-mundo for the article post. Awesome.

Thanks again for the article post.Really looking forward to read more. Really Cool.

visit this site and be up to date all the time.

I truly appreciate this blog.Really looking forward to read more. Really Cool.

Looking forward to reading more. Great blog.Really looking forward to read more. Want more.

So pleased to possess discovered this submit.. Seriously useful perception, appreciate your posting.. Appreciate the posting you given.. indeed, analysis is paying off.

Im grateful for the article post.Much thanks again. Keep writing.

This information is worth everyone as attention. Where can I find out more?

Just a smiling visitor here to share the love (:, btw great pattern.

Say, you got a nice article.Thanks Again. Want more.

I truly appreciate this blog post.Really thank you! Great.

Very neat article post.Really looking forward to read more. Really Cool.