Arithmetic and geometric progression

[Math Tutor]

Suppose a, b, c are integers and form an arithmetic progression. The same numbers form a geometric progression in different order. Prove that [tex]a^2 + b^2 + c^2[/tex] is divisible by 21.

[Guest]

Am I the only one that provide with answers for Math Problem of the Week section? It's not fair
I give all answers.This time I'll let another persons to offer the expected answer.


Y0uRShAD0W

[Math Tutor]

You always write some suggestions and does not provide solutions. Sometimes your suggestions are even wrong.

[Guest]

Was the solution for the previous problem (e.g.) just a simple suggestion? You said that I do this way
always. Moreover, my suggestions are even wrong. A really funny message from your side. I expect more
messages of this kind.


YS (If the rest of ppl won't be able to solve it then I'll provide with an answer as ALWAYS)

[Guest]

It's sad to see that no one is able to solve such an easy problem. If someone needs a hint from me, just ask for it.

[Guest]

(-2k, k, 4k)

[Guest]

True. That's patently obvious: a^2 + b^2 + c^2 = 21*k^2.