Hi! I've got a problem with this assignment. I really hope you can help me.
Find all such pairs of different natural numbers that
is divisible by
But then . Thus , and we only have to investigate the possibilities a = 1, 2 or 3.
When a = 1, the condition that divides becomes: divides , so that must be a factor of 24. You can then check that there are only three such values for b (given that b is different from a). Similar calculations (I'll leave you to work out the details) show that there are no solutions for a=2, and only one solution for a=3.
For a=2, you should get the condition that 2b+8 divides 4(b–2). Therefore b+4 divides 2(b–2) = 2(b+4) – 12. So b+4 divides 12. The only divisors of 12 which are greater than 4 are 6 and 12, and neither of these gives a solution to the problem.