# Thread: Finding the greatest prime factor:

1. ## Finding the greatest prime factor:

Find the greatest prime factor of:
4^17 - 2^28

Of course it can be done the long way (or with a calculator), but there's definitely a shortcut I'm missing. Can anyone lead me in the right direction? And this question supposedly doesn't need to use anything beyond simple algebra...

2. Does this help: 4^17 – 2^28 = 2^34 – 2^28 = 2^28(2^6 – 1)?

3. Originally Posted by thumpin_termis
Find the greatest prime factor of:
4^17 - 2^28

Of course it can be done the long way (or with a calculator), but there's definitely a shortcut I'm missing. Can anyone lead me in the right direction? And this question supposedly doesn't need to use anything beyond simple algebra...
4 = 2^2

So...

4^{17} - 2^{28} = [2^2]^{17} - 2^{28}

= 2^{34} - 2^{28}

= 2^{28}*2^{6} - 2^{28}

= 2^{28}*(2^6 - 1)

= 2^{28}*63

= 2^{28}*3^2*7

So 7 is the largest prime factor.

-Dan

4. There is nothing like completely giving away a good problem!
That must be the difference in physics and mathematics.

5. Originally Posted by Plato
There is nothing like completely giving away a good problem!
That must be the difference in physics and mathematics.
Nah. I just have found it easier to demonstrate the whole solution method while on this site. (However, had I known you had posted an answer before me I would have let you handle it in your style. I didn't see that you had until I saw your last post here. Apologies!)

-Dan

6. Originally Posted by topsquark
Apologies! -Dan
Acknowledged of course! And thank you.
I am really aware of this problem with help sites such as this.
Having spent 43 years working with mathematics students and having been a product of the Moore/Wall school of mathematics education, I have a real problem with what happens at many of the so-called ‘math-help sites’. There are two who contribute here. One is voted the ‘best-helper’. But in my view, that person simply needs to show the rest of us that he/she knows how to work the problem. How can handing a person a completely worked out solution really be considered teaching? That, I failed to ever understand. I do under grandstanding.

There is one other who does that here. I think that he/she is a fellow student who is trying to simply exceed ChapBlack in thankyous. What a pity it comes to that!

7. Originally Posted by Plato
Acknowledged of course! And thank you.
I am really aware of this problem with help sites such as this.
Having spent 43 years working with mathematics students and having been a product of the Moore/Wall school of mathematics education, I have a real problem with what happens at many of the so-called ‘math-help sites’. There are two who contribute here. One is voted the ‘best-helper’. But in my view, that person simply needs to show the rest of us that he/she knows how to work the problem. How can handing a person a completely worked out solution really be considered teaching? That, I failed to ever understand. I do under grandstanding.

There is one other who does that here. I think that he/she is a fellow student who is trying to simply exceed ChapBlack in thankyous. What a pity it comes to that!
Now Plato, believe me when I say, I have the utmost respect for you, but I could not let this comment of yours go unanswered. I realize that you are concerned with whether or not the people who ask for help around here really learn, as opposed to just copying down answers, and that is a noble concern, however I believe it is too noble for this context. Last time I checked, this was not a community of teachers, it is a place for people who love math and enjoy doing it even when they don’t have to (this excludes the people who just come to ask for help of course). And though I share your concerns somewhat, I realize that it is not our responsibility to teach the people who come here, it is their teachers’ responsibility, we are just here to provide a little extra help doing what we love to do. I do not appreciate how you come up with unflattering motives for why members contribute on this site, and found the way you described the infamous “two” particularly distasteful.

Now to directly address your problem with “so-called ‘math-help sites’” I will say this. It is possible for students to learn almost, if not just as much, from complete solutions as they would from small clues nudging them in a particular direction. If you ever take time to notice how the “best helper” and the “other one” respond to problems, you would realize that they almost always try to explain every step that they take when working out a problem. Often times they would give an introduction to the topic and even explain the general method before they use it, they don’t just vomit out answers. Furthermore, they encourage people to ask questions if anything is unclear and often advise students to practice other similar problems and get back to them about it. I know that I personally have learnt a lot just reading through the solutions of the best helper, and I’m sure others have as well. If a student thinks they can get by just copying answers, then that is their misfortune, the best helper and the “other one” should not be blamed for that.

And by the way, what benefit is it to the “other one” to surpass CaptainBlack in thank yous? Such a goal would not prove anything! I know for a fact that that has never been and still isn’t his motive for contributing to this site.

8. Thanks to both of you. I actually did try out the problem first by myself with Plato's hints and was able to come up with the answer, but of course, a complete solution is also definitely appreciated.

It's just the initial setup that really gets me with these type of problems (I suppose that's the way it's supposed to be.)

Thanks again guys.

9. Originally Posted by Plato
Acknowledged of course! And thank you.
I am really aware of this problem with help sites such as this.
Having spent 43 years working with mathematics students and having been a product of the Moore/Wall school of mathematics education, I have a real problem with what happens at many of the so-called ‘math-help sites’. There are two who contribute here. One is voted the ‘best-helper’. But in my view, that person simply needs to show the rest of us that he/she knows how to work the problem. How can handing a person a completely worked out solution really be considered teaching? That, I failed to ever understand. I do under grandstanding.

There is one other who does that here. I think that he/she is a fellow student who is trying to simply exceed ChapBlack in thankyous. What a pity it comes to that!
You have a good point and I don't deny it. My direction toward teaching on this site is that many of the (serious) students that come here because they have already tried the problem and failed to be able to do it, or have already asked a TA or the professor/teacher and not been able to understand them. In such cases where I have been teaching my own class I have found that the student usually needs a full explanation rather than the "Socratic" method I tend to usually employ.

The other class of student here is the one that is only interested in getting their homework done for them. I suppose I am doing them a disservice by working the problem for them, but if that's all they want they'll fail the course anyway because they haven't put any effort into it. Since I don't have face to face contact with them I can't really help them learn that lesson in a less self-destructive way anyway.

I have to go, so I can't quite finish this. (I suppose that's a good thing...I don't wish to write a book! )

-Dan

10. Originally Posted by topsquark
You have a good point and I don't deny it. My direction toward teaching on this site is that many of the (serious) students that come here because they have already tried the problem and failed to be able to do it, or have already asked a TA or the professor/teacher and not been able to understand them. In such cases where I have been teaching my own class I have found that the student usually needs a full explanation rather than the "Socratic" method I tend to usually employ.

The other class of student here is the one that is only interested in getting their homework done for them. I suppose I am doing them a disservice by working the problem for them, but if that's all they want they'll fail the course anyway because they haven't put any effort into it. Since I don't have face to face contact with them I can't really help them learn that lesson in a less self-destructive way anyway.

I have to go, so I can't quite finish this. (I suppose that's a good thing...I don't wish to write a book! )

-Dan
I completly agree with you topsquark. That's one of the reasons i often give complete solutions. i try to explain each step so i save the ones that come just to get their hoemwork done from themselves...i think it works sometimes, because from the explanation they may realize that the stuff is not that hard, and may actually try to get it on their own afterwards.

was that comment about writing a book aimed at me? i was just venting, dont worry about it

11. I just do problems how I feel like doing them. I skip steps because I am lazy.

But I have to add, if you ever read serious math books, note how they skip steps in proofs at times. Sometimes they manage to make 6 lines into a full page when written out in full detail (especially in algebra books).

12. Well, coming from someone who comes here every once in awhile to get help my own help on math, I learn through both ways. Sometimes, I am completely lost in a problem, and I find that I learn much better from someone simplfy showing all their steps and solving the problem for me (even if I had no idea how to solve it in the first place.) With all the steps in front of me, I can usually sit there and read through it and figure out where everything came from. I actually enjoy learning this way better.

And of course, getting hints and nudges in the right direction work well, too, but neither method is wrong or bad and neither should be dissed.