It is known that a, B and C are all integers. For any integer x, the value of the algebraic expression AX2 + BX + C can be divisible by 3. It is proved that ABC can be divisible by 27

It is known that a, B and C are all integers. For any integer x, the value of the algebraic expression AX2 + BX + C can be divisible by 3. It is proved that ABC can be divisible by 27

It is proved that when x = 1, a + B + C can be divisible by 3; when x = - 1, A-B + C can also be divisible by 3,
Ψ B is divisible by 3
Ax1 & # 178; + BX1 + C - (AX2 & # 178; + bx2 + C) = a (x1 & # 178; - x2 & # 178;) + B (x1-x2) can be divisible by 3 (x1 ≠ X2, x1-x2 may not be divisible by 3)
A is divisible by 3
∵ a + B + C can be divided by 3
C can also be divided by 3
The ABC is divisible by 27