Find the positive integer solutions of the equation
æ
ç
è 		1 + 1
a
 ö
÷
ø 		æ
ç
è 		1 + 1
b
 ö
÷
ø 		æ
ç
è 		1+ 1
c
 ö
÷
ø 		= 2.
[Both this problem and the problem Proximity come from the Hungarian magazine KoMaL and you'll find many other challenging problems in English on the KoMal website ]