## Can we construct three irrational numbers a,b,ca,b,c such that a+b+c∈Qa+b+c \in \mathbb Q?

This is rather easily shown to be possible if no constraint is put on a,b,c. However, is it also possible under the following constraint: a,b and c can not be rational multiples of each other. If that constraint is too tight to allow such a construction, would it be possible if we loosen it a … Read more