Ta có A = 1 + 3 + 32 + 33 + ... + 330
\(\Rightarrow3A=3+3^2+3^3+3^4+...+3^{31}\)
\(\Rightarrow3A-A=\left(3+3^2+3^3+3^4+...+3^{31}\right)-\left(1+3+3^2+3^3+...+3^{30}\right)\)
\(\Rightarrow2A=3^{31}-1\)
\(\Rightarrow A=\frac{3^{31}-1}{2}\)
Ta có 331 - 1 = 328.33 - 1 = (34)7 . 27 - 1 =
= (...1)7.27 - 1 = (...1).27 - 1 = (...7) - 1 = (...6)
\(\Rightarrow A=\frac{3^{31}-1}{2}=\frac{\overline{...6}}{2}=\overline{...3}\)
\(\Rightarrow\)A không là số chính phương