+0

+1
309
14
+89

Given that 1000343 has two distinct prime divisors p and q, find (p+q)

Basically what I've done is said that if x=10, then 1000343 = x^6 + 3x^2 + 4x + 3

and usually I would factor from here, but I don't know how.

:)

Oct 12, 2022

#1
+118616
+1

You could just use a calculator.

factor(1000343) = 107*9349

Oct 12, 2022
#2
+89
+2

Without a calculator lol

I know, 107 and 9349, but like we don't have fancy calculators in math contests

Also this is under the unit of factoring

And I kinda need work, not just an answer

But ty

AutumnStorm  Oct 12, 2022
#4
+1

Try something like this:

1,000,343 ==1,000,000 + 343

[1,000,000 + 343]^(1/3) ==[100 + 7]==107 - since this is a prime number, then it must be one of the prime factors.

Then by simple long division: 1,000,343 / 107 ==9,349 - this must be the 2nd prime factor.

Oct 12, 2022
#6
+2440
-4

OMG Mr. BB! What a pile of Bullshit! This ranks in your top three (3) piles of bullshit for the current calendar year.

I’d asked if you had a stroke, but this is just bloody normal for you.

GA

--. .-

GingerAle  Oct 12, 2022
edited by Guest  Oct 12, 2022
#7
+2667
0

Who's Mr.BB? Is it me?

BuilderBoi  Oct 12, 2022
#8
+89
+1

Thanks :) Basically, I need to see that 343 is a perfect cube.

Not me feeling kinda dumb rn lol

:) :)

AutumnStorm  Oct 12, 2022
#11
+2440
-4

OK Stormy, I’ll answer ...with some advice: One thing that will help is to understand the differences between prime divisors (aka: prime factors), divisors (aka: factors), and factoring polynomials. Based on your post above, you do not presently know these differences.   Knowing what you are looking at and what you need will help you discern the path needed to find a solution process.

I’ll add that Mr. BB’s solution path will lead you into a world of chaos. At present, you are too dumb to know this. Unless you are a dung beetle larva, avoid Mr. BB’s math magic, pixie dust, bullshit answers. If you are dung beetle larva, you may find this nutritious and delicious, but you will not learn any useful math from any of the BBs.   https://web2.0calc.com/questions/hallppp-3-questions

Here’s another example of how Mr. BB bullshits.

Though his comments may be true, they are only true by tautology. They are not very useful for this particular problem, and they are useless for any related problem.  No one learns anything from Mr. BB’s Blarney, except how to become a Blarney Master.  He is one too. . . . One of the best I’ve seen. https://web2.0calc.com/questions/nice-question#r9

Hapless bystanders are drawn into this mush. It’s not criminal, but it needs a warning sign: Fallacious Math and Malicious Logic ahead. Proceed with caution!  https://web2.0calc.com/questions/hallppp-3-questions#r16

GA

--. .-

GingerAle  Oct 14, 2022
edited by GingerAle  Oct 14, 2022
#12
+2440
-4

Who's Mr.BB? Is it me?

NO! LOL! It’s not you, BuilderBoi. You are a wonderful mathematician. You have occasional chaotic ideas for solving certain problems. I suppose this is because thinking outside the box can sometimes lead one into a parallel dimension of spacetime, which can be absurd in normal spacetime. These types of ideas can be quite funny though, which compels a humorous ball-busting troll post.

The Mr. BBs are pseudo-mathematicians. They often present fake math in the form of pseudo mathematical prestidigitation. Mr. BB is the stubborn, relentless, intractable Blarney Banker of lore: a pseudo intellectual with a multiplicity of advanced dimwit degrees in arrogant stupidity; a professor of misinformation, who teaches with authority and irritation. Source.

Over the years, there have been four of them on this forum. The original Mr. BB is the Blarney Banker. The “Banker” name came from his fondness for answering interest rate questions. There are (were) three other BBs, with two who have not been in attendance lately: Blarney Bag, Bubble Brain, and the Bullshit Bug. The Bullshit Bug is a genetic variant of the dung beetle that, instead of rolling dung into a ball, it spreads it all over the forum. Source

I sometimes refer to Mr. BB (1 or 2) as “!!!Mr. BB”. (Read as Triple Deranged Mr. BB) source: https://web2.0calc.com/questions/solve-for-a-in-terms-of-b-amp-c#r6

Here’s a post from June 2018 that list links to some of Mr. BB’s posts. In this thread I mistakenly trolled the guest-posting-EP as Mr. BB.  It’s quite funny, but not as funny as this post where I troll Ron (a long-time guest poster). I will sometimes mistake a post as coming from a BB when the presented solution resonates with certain modulated frequencies resembling a mix of gobbling turkeys and quacking ducks.

Most of the early posts where I troll Mr. BB had dialogue, but many were hidden by one or more moderators. Here’s a main thread post where I present Mr. BB with a Christmas gift.  Mr. BB (Blarney Banker) quit responding to my troll posts a few years ago, but his profound dumbness continues to this day.

The other BBs continued to respond, at least occasionally. Here’s a post where I troll Mr. BB (#4 -Bullshit Bug) and the Blarney Master. Also in this thread I define a basic personality profile for the BBs.

Here’s my first troll post for Mr. BB, and here’s a very early post, (shortly before I started addressing him as Mr. BB). I introduce my dog, Mr. Peabody, and cat, DC Copper in this post. They are both ‘hams’ and like to have cameos appearances in troll posts.  It’s amazing how much a dog and cat can augment the satirical humor of a genetically enhanced chimp’s troll post.

https://web2.0calc.com/questions/working-with-formulas-help

https://web2.0calc.com/questions/rolling-dice

Mr. Peabody and DC Copper join in to troll a potential Mr. BB. (This was probably BB #3 Bubble Brain –I’m not sure. He didn’t post very often.)

Here JB reproduces a ‘play’ I wrote to satirize Mr. BB’s and Mathking’s conversation. Blip and Bleep were chosen because the names start with Bs. Note also (in my response to JB) that Mr. BB’s posts are significant enough to give him a Category (zero of course)

*Category (0) –Mr. BB Interest Rate questions or arcane questions optimally answered with Monty Carlo style or tabulated, logical resolution computer code

In the early days, Mr. BB answered numerous basic interest rate questions.  Later, arcane questions, which often were only answerable using a computer, started appearing. He’d post these questions and the computer-generated solution. The solutions weren’t always correct, such as the one described below.

Here’s Rom’s introduction to Mr. BB. I initially hung a lantern on this post (without explicitly identifying Mr. BB) to present an alternative solution method. I wasn’t sure if Rom would comment or not.  When he did, I turned up the light and illuminated Mr. BB and his BS.

Rom is an amazing engineering-class math mathematician.  I wish he’d return!

More than presenting moronic math solutions and being obnoxious and irritating, the BBs can be quite rude: https://web2.0calc.com/questions/help_87550

I’m not the only one who trolls the BBs. JB also trolls Mr. BB: here and here are two examples. There are more if you’d care to search.

Nauseated also trolled him once, comparing Mr. BB’s chemistry skills to those of Sorasyn. The Sorasyn post is one of the funniest troll posts on the forum.

The first person to troll Mr. BB was Dragonlance. There are several posts where DL responds to, retorts, and trolls Mr. BB.  This is his best one.

https://web2.0calc.com/questions/melody-what-are-some-of-the-amazing-things-that-your-ohline-can-do-and-that-my-hp-scientific-calculator-can-t-do#r3  I made comments in reference to this post here and here.

Here’s another post where DL tells the anonymous Mr. BB to “STFU!!!!!!!!!!!!”  Eloise thought this was quite funny. I do too!

The BBs are the most trolled and troll-worthy individuals on the forum. I do not believe you could descend to their level, even if you tried. Not that you’d ever want to.

GA

--. .-

GingerAle  Oct 14, 2022
edited by GingerAle  Oct 14, 2022
#9
+1

AutumStorm:

Please note that your number can be expressed as the sum of 2 perfect cubes. That is:

1000343 = 100^3 + 7^3  and  100 + 7 =107. This 107 is ALWAYS a divisor of 1000343. That is, 107 divides

1000343 evenly with no remainder. Then, the only thing you have to determine is to find out whether 107 is a prime number or not. If you don't know whether it is a prime or not, you may try the sieve method of trying to divide it by all prime numbers from 2 to sqrt(107) ==<11, which is only 4 such primes (2, 3, 5, 7). You will quickly see that it is not divisible by any of the 4 primes. Therefore, it must be a prime number. Good Luck.

Oct 12, 2022
#10
+89
+1

Thanks :)

I didn't notice that 343 was a perfect cube lol

AutumnStorm  Oct 12, 2022
#13
+2440
-5

Minor Analysis of The Sum of Two Perfect Cubes and the Loss of Mathematical Virginity

Mr. BB: Please note that your number can be expressed as the sum of 2 perfect cubes.

Stormy: Ok, so how am I supposed to know that?

Mr. BB: Just sprinkle some third-root math-magic pixie dust on it and the 343 lights up.

Now subtract the 343 from the 1000343 leaving 1000000, and the residual pixie dust lights up the 1000000 because it had an integer cube root too.

Stormy: OK, so now I know 343 and 1000000 are perfect cubes. But no calculators are allowed, so how do I find the third roots?

Mr. BB: Just give the pixie dust some time; it will naturally resolve them to 7 and 100, faster than you can say transgender ...I mean transmografier. After it does this, just add the two numbers together, then test if it’s prime. If it is, then divide the original number by 107 and that will give you the other prime.

Stormy: Does the pixie dust do that?

Mr. BB: No. you have to do that yourself.

Stormy: Oh, OK. That doesn’t seem too hard for small numbers.

Mr. BB: Now you know how to do this. Good luck.

------------------------

Stormy: Ah... Mr. BB, I tried your magic pixie dust on these numbers that are the product of two primes, but it didn’t work!

107 * 9377 = 1003339

107 * 9391 = 1004837

107 * 9397 = 1005479

107 * 9403 = 1006121

107 * 9413 = 1007191

107 * 9419 = 1007833

107 * 9421 = 1008047

107 * 9431 = 1009117

107 * 9433 = 1009331

107 * 9437 = 1009759

107 * 9439 = 1009973

113 * 9377 = 1059601

127 * 9391 = 1192657

131 * 9397 = 1231007

137 * 9403 = 1288211

Mr. BB: You carefully sprinkled the pixie dust on them?

Stormy: Yes, I did.

Mr. BB: Then there aren’t any perfect cubes that sum to these numbers.

Stormy: So what do I do?

Mr. BB: You have to use a different pixie dust; it’s very expensive, and I’m out of it.

Stormy: You’re out of it, alright! You’re a senile asshole!

Mr. BB: People keep telling me that, but I don’t believe them. Most everyone else doesn’t believe it either.   Now run along and play; I have important things to do. Oh, before you go, can you sing Stormy Weather for me? I like the song....

Stormy: Go fuck yourself!!!

Mr. BB: I’ve been doing that for years. I prefer to it to others: I like mathematical virgins; I just tickle their fancy, so they don’t realize they’re being fucked until it’s too late. Been doing it for years.... It’s never as good for them as it is for me, but it is good for me.... If you are not going to sing for me, then move along.... Like I said, I have important things to do.

******

GA

--. .-

GingerAle  Oct 14, 2022
edited by GingerAle  Oct 14, 2022
#14
+118616
+3

I have no idea if anbody has actually answered this yet but here is a 'proper' answer.

We can see that    1000343 = 1000000 + 343 = \(100^3+7^3\)

I know that   \(a^3+b^3=(a+b)(a^2-ab+b^2)\)

a=100   and b=7

1000343=(100+7)(10000-700+49)

1000343=(107)(9349)

Oct 14, 2022