Olympiad Problem

any more restrictions?
e.g. "a, b, c are integers"

2012-12-18 14:33:29 補充：
sub. c = 2 - a - b into abc = 4
ab(2 - a - b) = 4
ab^2 + a(a - 2)b + 4 = 0
for b is real, [a(a - 2)]^2 - 4(a)(4) >= 0
a^2(a - 2)^2 - 16a >= 0
a^4 - 4a^3 + 4a^2 - 16a >= 0
a(a^3 - 4a^2 + 4a - 16) >= 0
a(a - 4)(a^2 + 4) >= 0
a <= 0 or a >= 4

2012-12-18 14:34:06 補充：
a can be -ve infinity

a doesn't have any minimum value
a can be extremely small
a can be -1 -2 -3.......-9999999999.......

Without any further info, a has no min.