Question 142
Show that the positive divisors of no integer greater than $1$ may be placed in the cells of a rectangular array so that the four conditions below be simultaneously fulfilled:
(a) each cell contains exactly one divisor;
(b) distinct cells contain distinct divisors;
(c) the sum of the divisors on each row is the same; and
(d) the sum of the divisors on each column is the same.
(a) each cell contains exactly one divisor;
(b) distinct cells contain distinct divisors;
(c) the sum of the divisors on each row is the same; and
(d) the sum of the divisors on each column is the same.