Consider the equation
1
a
 + 1
b
 + 1
c
 = 1
where a, b and c are natural numbers and 0 < a < b < c. Prove that a < 3 and also that b < 4 and hence that there is only one set of values which satisfy this equation.

Find the six sets of values which satisfy the equation
1
a
 + 1
b
 + 1
c
 + 1
d
 = 1
where a, b, c and d are natural numbers and 0 < a < b < c < d.