How can prove $\frac{x_n}{n}+\frac{ x_{n-1}}{n-1}+...+\frac{x_3}{3}+\frac{y_m}{m}+\frac{ y_{m-1}}{m-1}+...+\frac{y_3}{3} \ge 1$

Question

Let $A, a, b$ be positive integer numbers, $gcd(a,b)=1; a\ne b$ and

$A=x_na^n+x_{n-1}a^{n-1}+....+x_3a^3 =y_mb^m+y_{m-1}b^{m-1}+....+y_3b^3$

Where $x_i \in 0, 1, 2,..., a$ and $y_j \in 0, 1, 2,..., b$, and $n, m \ge 3$, $x_n \ne 0$, $y_m \ne 0 $

How can prove that:

$$\frac{x_n}{n}+\frac{ x_{n-1}}{n-1}+...+\frac{x_3}{3}+\frac{y_m}{m}+\frac{ y_{m-1}}{m-1}+...+\frac{y_3}{3} \ge 1$$

Can you help me?

See also:

• Hexadecima
• Decima