Abstract
In this paper we computed all the 379 118 solutions of the equation ∑ i = 1 k 1 x i = 1 in distinct odd natural numbers for k = 11 . We provide a lower bound for the number of solutions of ∑ i = 1 13 1 x i = 1 . Also, we answer similar questions about the equation ∑ i = 1 k − 1 1 x i + 1 lcm ( x 1 , … , x k − 1 ) = 1 . Finally, we prove some results concerning optimization of x 1 and x 11 .
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