Question 61
a. We have seven positive integers $a, b, c, d, e, f, g$ such that the products $ab, bc, cd, de, ef, fg, ga$ are all perfect cubes. Prove that $a, b, c, d, e, f, g$ are also perfect cubes.
b. We have six positive integers $a, b, c, d, e, f$ such that the products $ab, bc, cd, de, ef, fa$ are all perfect cubes. Is it always true that $a, b, c, d, e, f$ are all perfect cubes?
Note: an integer $m$ is called a perfect cube if $m = n^{3}$ for some integer $n$.
b. We have six positive integers $a, b, c, d, e, f$ such that the products $ab, bc, cd, de, ef, fa$ are all perfect cubes. Is it always true that $a, b, c, d, e, f$ are all perfect cubes?
Note: an integer $m$ is called a perfect cube if $m = n^{3}$ for some integer $n$.