Since AB is a multiple of 4, there are two possibilities;

Case 1. One of them, A or B, is odd and the 
other a multiple of 4. 

Case 2. Both A and B are even

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Case 1: Say A is a multiple of 4 and B is odd

A = 4p,  B = 2q-1, for some positive integers p and q














So 4 must be divisible by 2q-5

2q-5 = 1,2, or 4
  2q = 6,7, or 9

Since 2q is even, it can only be 6
  2q = 6
   q = 3







A = 4p,    B = 2q-1
A = 4(5)   B = 2(3)-1
A = 20     B = 6-1
A = 20     B = 5

Checking 

One solution is {A,B} = {20,5}

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Case 2:  Both A and B are even

A = 2p,  B = 2q, for some positive integers p and q

















So 4 must be divisible by q-2

q-2 =  1; 2; 4 
  q =  3; 4; 6 

Substitute in 

  p =  6; 4; 3
  A = 12; 8; 6 
  B =  6; 8;12

A and B are different, so that rules out the 8's,
so one is 6 and the other 12.

Checking: 

So there are two solutions:

{A,B} = {20,5}

and

{A,B} = {12,6}

Edwin