mjhjmtu

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Clash Royale CLAN TAG #URR8PPP up vote 17 down vote favorite 6 Out of all the questions I answered in a math reviewer, this one killed me (and 7 more). Let $J, K, L, M, N$ be five distinct positive integers such that $$ frac1J + frac1K + frac1L + frac1M + frac1N + frac1JKLMN = 1. $$ Then, what is $J + K + L + M + N$ ? I have been thinking about this for nearly 6 days. algebra-precalculus share | cite | improve this question edited yesterday Especially Lime 20.9k 2 26 55 asked yesterday Heroic24 127 7 13 Is $JKLMN$ a product or a number obtained by writing $J,K,L,M,N$ next to each other? – yurnero yesterday 3 Regardless of whatever $JKLMN$ might mean (though you should clarify), it is easy to get some quick estimates. Assuming $J<K<L<M<N$, it is pretty easy to see that $Jin 2,3$. I'd work along those lines. – lulu yesterday 4 $2, 3, 11, 23, 31$ satisfies. I coded a simple prog