Give an example?

Question

I am giving an example where sum of three perfect squares are sum of other three perfect squares
9^(2) + 2^(2) + 2^(2) = 4^(2) + 3^(2) + 8^(2)
i.e. a^(2) + b^(2) +c^(2) = d^(2) + e^(2) + f^(2)
But here i am getting "b" & "c" as same.Give an example where "a", "b" ,"c" ,"d", "e" & "f" are distinct from each other.I would say that there is no such example .What do u say & why?

Answer 1

with n a perfect square represent n as x^2 + p with prime p = 1 mod 4 and write p = y^2 + z^2. This yields the representation n = x^2 + y^2 + z^2.
the largest n for wicht this is not possible is 9634

How serious are you with your questions ?
see http://answers.yahoo.com/question/index;_ylt=AvivP2vdn_qSdnT5M_Siyhfsy6IX?qid=20061106081029AAr4yHJ

your chooses answer is not an answer

Answer 2

try this
a = 0 d = 2
b = 3 e = 4
c = 6 f = 5

=> a^(2) + b^(2) +c^(2) = 0+9+36= 45
=> d^(2) + e^(2) + f^(2) = 4+16+25= 45

so u see there is a counter example to show tht u r wrong if u say there is no such example.

Answer 3

Good one.....rajesh