Got Homework?
Connect with other students for help. It's a free community.
Here's the question you clicked on:
 0 viewing
Find all positive integer pairs (x,y) such that 4xyxy is a perfect square.
 one year ago
 one year ago
Find all positive integer pairs (x,y) such that 4xyxy is a perfect square.
 one year ago
 one year ago

This Question is Closed

mukushlaBest ResponseYou've already chosen the best response.0
without loss of generality we can suppose \[y\ge x \]because the expression is symmetric
 one year ago

mukushlaBest ResponseYou've already chosen the best response.0
assume that \[y=x+a\]with \(a\ge 0\)
 one year ago

RolyPolyBest ResponseYou've already chosen the best response.1
Okay! I'll try from here!!
 one year ago

mukushlaBest ResponseYou've already chosen the best response.0
wait ... im afraid i made a mistake :/
 one year ago

RolyPolyBest ResponseYou've already chosen the best response.1
Don't be afraid :P \[4xyxy=4x(x+a)x(x+a)=4x^2+(4a2)xa\]
 one year ago

RolyPolyBest ResponseYou've already chosen the best response.1
\[\Delta=(4a2)^2  4(4)(a)=0\]\[16a^2  16a + 4 + 16a=0\]\[16a^2 + 4 =0\]Well well well...
 one year ago

shubhamsrgBest ResponseYou've already chosen the best response.0
4xyxy = (x+y)^2  (xy)^2  (x+y) = (x+y)(x+y1)  (xy)^2 i am not too sure if that'd help! :P
 one year ago

mukushlaBest ResponseYou've already chosen the best response.0
@RolyPoly ...Are you familiar with modular arithmetic??
 one year ago

RolyPolyBest ResponseYou've already chosen the best response.1
I've never heard of it! :(
 one year ago

shubhamsrgBest ResponseYou've already chosen the best response.0
i dont know much but i do have a little idea..will you please guide me/us through a solution @mukushla
 one year ago

RolyPolyBest ResponseYou've already chosen the best response.1
Forgive me for closing this question, even though it's not yet solved!
 one year ago
See more questions >>>
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.