Maths Olympiad Prep

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Algebra Difficulty 5.0 AIME, harder Prove it

3-4. Prove that for any positive integer nn the number n2+8n+15n^{2}+8 n+15 is not divisible by n+4n+4.

Solution

Solution 4. It is enough to notice that n2+8n+15=(n+4)21n^{2}+8 n+15=(n+4)^{2}-1.

\section*{8th grade}

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