Egyptian Fractions with Restrictions

Yong-Gao Chen, Christian Elsholtz, Li-Li Jiang

Let $T_o(k)$ denote the number of solutions of ${\sum }_{i=1}^k\frac{1}{x_i}=1$ in odd numbers $1<x_1<x_2<...<x_k$. It is clear that $T_o(2k)=0$. For distinct primes $p_1, p_2,..., p_t…