Here is a Math question :?

Question

Hello,
Could you tell me how many pairs of integers (a,b) are there with a = or < b that 1/6=1/a+1/b?

Thanks !
Alix Witvoet

Answer 1

a and b would both need to be positive since their sum and product is positive. 12 for a and b works so any other pairs must have a < 12 since if a went up, b would have to go down. And a must be greater than 6 or else 1/a would be greater than or equal to 1/6 and 1/b would have to be negative or zero. 1/6 - 1/a = 1/b so try a for 7, 8, 9, 10, 11

1/6 - 1/7 = 1/42 so 7 and 42
1/6 - 1/8 = 1/24 so 8 and 24

etc

Answer 2

1/6=1/a+1/b
(a+b)/ab=1/6

6(a+b)=ab

a=b
or
a