Question 42
Let $a$ and $n$ be two fixed positive integers.
a) Prove that there exist $n$ positive integers $a_1, a_2, \dots, a_n$ such that
$$
1 + \frac{1}{a} = \left(1 + \frac{1}{a_1}\right) \left(1 + \frac{1}{a_2}\right) \dots \left(1 + \frac{1}{a_n}\right).
$$
b) Prove that $1 + \frac{1}{a}$ has only finitely many possible representations as in the point a).
a) Prove that there exist $n$ positive integers $a_1, a_2, \dots, a_n$ such that
$$
1 + \frac{1}{a} = \left(1 + \frac{1}{a_1}\right) \left(1 + \frac{1}{a_2}\right) \dots \left(1 + \frac{1}{a_n}\right).
$$
b) Prove that $1 + \frac{1}{a}$ has only finitely many possible representations as in the point a).