A community for students.
Here's the question you clicked on:
 0 viewing
anonymous
 3 years ago
for how many integers \(m\) the expression\[1+m+m^2+m^3+m^4\]becomes a perfect square?
anonymous
 3 years ago
for how many integers \(m\) the expression\[1+m+m^2+m^3+m^4\]becomes a perfect square?

This Question is Closed

anonymous
 3 years ago
Best ResponseYou've already chosen the best response.01+m+m^2(1+m+m^2) \[1+m+m ^{2}(m+1)^{2}\]

anonymous
 3 years ago
Best ResponseYou've already chosen the best response.0it will be perfect square for m=0 only

John_ES
 3 years ago
Best ResponseYou've already chosen the best response.0Well, numerically I find others m not zero, m=1,m=0 and m=3. A more rigorous proof is needed for all m in integers.

anonymous
 3 years ago
Best ResponseYou've already chosen the best response.01+m(m+1)+m^3(m+1)=1+(m+1)(m+m^3) =1+(m+1)(m^2(m+1)) =1+(m^2)*(m+1)^2 =1+(m(m+1))^2 except zero it will not be a perfect square bcoz after sqauring 1is added which makes it a perfect square

shubhamsrg
 3 years ago
Best ResponseYou've already chosen the best response.1you have done a mistake in your 2nd step @gorvs

Loser66
 3 years ago
Best ResponseYou've already chosen the best response.0all you are off line, I can write whatever I like, I choose (m^2 +1) ^2 as my perfect square, so \[(m^2+1)^2=m^4+2m^2+1\] to find out the solution, I let \[m^4+2m^2+1=m^4+m^3+m^2+m+1\] so, when \[m^2=m+m^3\], I have perfect square \[m^2=m^2(\frac{1}{m}+m)\] > \[\frac{1}{m}+m=1\] \[m^2m+1=0\]no real solution for this.

shubhamsrg
 3 years ago
Best ResponseYou've already chosen the best response.1I got a method but not too sure if its ideal lets take 1+ m + m^2 + m^3 + m^4 = p^2 for some integer p then m(1+m) + m^3 (1+m) = (p+1) (p1) m(1+m)(1+m^2) = (p+1)(p1).1 now comparing will get our answers, but it'll be bit lengthy as too many permutations possible like this one yields m=3 and p=11 m(1+m) = 1+p (1+m^2) = p1 like wise we will make all possible comparisons and try to find out integer solutions

anonymous
 3 years ago
Best ResponseYou've already chosen the best response.0i asked you this before @mukushla

anonymous
 3 years ago
Best ResponseYou've already chosen the best response.0really, i cant remember, nice one :)

anonymous
 3 years ago
Best ResponseYou've already chosen the best response.0http://openstudy.com/users/jonask#/updates/50783e67e4b02f109be41dff

anonymous
 3 years ago
Best ResponseYou've already chosen the best response.0so do u know complete solution now?

anonymous
 3 years ago
Best ResponseYou've already chosen the best response.0well somehow i gave up and jus considered the fact that it is between two perfect squares so m=3
Ask your own question
Sign UpFind more explanations on OpenStudy
Your question is ready. Sign up for free to start getting answers.
spraguer
(Moderator)
5
→ View Detailed Profile
is replying to Can someone tell me what button the professor is hitting...
23
 Teamwork 19 Teammate
 Problem Solving 19 Hero
 Engagement 19 Mad Hatter
 You have blocked this person.
 ✔ You're a fan Checking fan status...
Thanks for being so helpful in mathematics. If you are getting quality help, make sure you spread the word about OpenStudy.