## Problem of the Day #237: Eleven Eleven ElevenNovember 11, 2011

Posted by Saketh in : potd , trackback

Alex is thinking of $111111$ numbers $a_1, a_2, a_3, …, a_{111111}$ such that

$$a_1+a_2+a_3+…+a_{111111} = 111111$$ $$a_1^3 + a_2^3 + a_3^3+…+a_{111111}^3 = a_1^4 + a_2^4 + a_3^4+…+a_{111111}^4$$

Find all distinct sequences of numbers that he could be thinking of.

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