| Thread Closed |
(n^4) + 4 is composite ? |
Share Thread | Thread Tools |
| Apr19-04, 10:03 PM | #1 |
|
|
(n^4) + 4 is composite ?
How do you prove that (n^4) +4 is composite for all n>1 ?
I found this problem in a book I was reading. The even n part is obvious. The proof for odd n cannot be done by trying to factorize [(2k+1)^4]+4. I know this is true, because I've tried and moreover, the factors of the first few such numbers are : (2*2*5),(5*17),(2*2*5*13),(17*37),(2*2*5*5*13),(5*13*37),... The expected factors of 4 appear in the even numbers, but the factors for the odds seem patternless. So, I imagine that the proof must be done by some other means. Any ideas ? |
| PhysOrg.com |
science news on PhysOrg.com >> Hong Kong launches first electric taxis >> Morocco to harness the wind in energy hunt >> Galaxy's Ring of Fire |
| Apr19-04, 10:06 PM | #2 |
|
|
Are there any factors that tend to occur frequently? Maybe you can solve the problem by cases.
|
| Apr20-04, 02:10 AM | #3 |
|
|
n=3: n^4+4 = 5*17 n=5: n^4+4 = 17*37 n=7: n^4+4 = 5*13*37 = 37*65 And I'll add n=9 for you: n=9: n^4+4 = 5*13*101 = 65*101 See any pattern yet? That should lead you to the general proof. |
| Apr20-04, 08:19 AM | #4 |
|
|
(n^4) + 4 is composite ?
thanks crag,
I must be blind ! |
| Apr20-04, 07:39 PM | #5 |
|
|
On no! The blind leading the blind!
|
| May27-04, 10:06 AM | #6 |
|
|
how about:
[tex]n^4 + 4 = n^4 + 4 - 4n^2 + 4n^2 = (n^2 + 2)^2 - (2n)^2 = (n^2 + 2n + 2)(n^2 - 2n + 2)[/tex] :) edit: sorry, i pulled up an old post... just realized that it's from April not May 20th... |
| May27-04, 10:41 AM | #7 |
|
|
I am almost tempted not to welcome you
|
| May27-04, 01:34 PM | #8 |
|
|
thanks, yrch...that's nice.
Now I really feel like $#!+. |
| Thread Closed |
| Thread Tools | |
Similar Threads for: (n^4) + 4 is composite ?
|
||||
| Thread | Forum | Replies | ||
| Composite Functions | Precalculus Mathematics Homework | 1 | ||
| Composite doubt......... | Materials & Chemical Engineering | 1 | ||
| Composite Derivative | Calculus & Beyond Homework | 2 | ||
| Composite filed | Quantum Physics | 3 | ||
| composite function | General Math | 18 | ||