Question 2
Show that any representation of $1$ as a sum of distinct reciprocals of numbers drawn from the arithmetic progression $\{2,5,8,11,\ldots\}$, such as the following example, must have at least eight terms:
$$1=\frac12+\frac15+\frac18+\frac1{11}+\frac1{20}+\frac1{41}+\frac1{110}+\frac1{1640}.$$
$$1=\frac12+\frac15+\frac18+\frac1{11}+\frac1{20}+\frac1{41}+\frac1{110}+\frac1{1640}.$$