# amazing problem

• September 15th 2012, 10:14 AM
geniusgarvil
amazing problem
a,b,c are 3 real nos. Prove that the 3 numbers a^2+b+c, b^2+a+c, c^2+a+b cannot be perfect squares altogether.
• September 15th 2012, 12:52 PM
CoffeeBird
Re: amazing problem
can you explain what you mean a little more? like, what do you mean by altogether?
• September 15th 2012, 01:06 PM
HallsofIvy
Re: amazing problem
I believe he means "cannot all be perfect squares".

geniusgarvil seems to have a "genius" for posting problems that are "amazing" only because they are wrong. In this case, $a= b= c= -1+\sqrt{5}$
have $a^2+ b+ c= b^2+ a+ c= c^2+ a+ b= 4$.
• September 15th 2012, 03:59 PM
richard1234
Re: amazing problem
Quote:

Originally Posted by geniusgarvil
a,b,c are 3 real nos. Prove that the 3 numbers a^2+b+c, b^2+a+c, c^2+a+b cannot be perfect squares altogether.

a = b = c = 0. 0 is a perfect square. Hmm.