Given nonnegative real numbers α and β, let be a multiset that generalizes Spec(α) = Spec(α; 0). Prove or disprove: If the m 3 multisets Spec(α 1 ; β 1 ), Spec(α 2 ; β 2 ), . . . , Spec(αm; βm)...

Given nonnegative real numbers α and β, let

be a multiset that generalizes Spec(α) = Spec(α; 0). Prove or disprove: If the m
3 multisets Spec(α₁; β₁), Spec(α₂; β₂), . . . , Spec(αm; βm) partition the positive integers, and if the parameters α₁
₂