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Out of eleven square integers we can pick six integers such that $a^2+b^2+c^2=d^2+e^2+f^2 \,(\mod 12)$

This was probably the toughest question in section b of our maths paper.I knew this question needs php but I couldn't bring the condition to enforce php. Please help me

J126
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Caratheodory_Enthusiast
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1 Answers1

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Hint: start by figuring out the only possible values of a square $\pmod {12}$.

user141592
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  • Sorry I didn't mentioned that I had done that it's just 0,1,4,9.then what to do. – Caratheodory_Enthusiast Mar 15 '15 at 16:06
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    Show that out of these four values one of the following must happen: there are three that occur two times each; one that occurs four times and another twice; or one that occurs six times. In each of these cases you can do it. – John Brevik Mar 15 '15 at 16:29