...of the Product of Two Algebraic Numbers One of Which Is of...
Let p be a prime number and let m be a positive integer such that 𝑝∤𝑚. Suppose that 𝛼,𝛽 are algebraic numbers such that deg(𝛼)=𝑚, deg(𝛽)=𝑝, and the minimal polynomial of β over ℚ is 𝑓(𝑥). (a) If 𝑝>2 and 𝑓(𝑥)≠𝑥𝑝+𝑐, where ...