Is the conjecture on A+B=C following correct ?

Conjecture:Let $A, B, C$ be three positive integer numbers such that $A+B=C$ with $\gcd(A, B, C) = 1$. By Fundamental theorem of arithmetic we write:$A=a_1^{x_1}a_2^{x_2}...a_n^{x_n}$,

$B=b_1^{y_1}b_2^{y_2}...b_m^{y_m}$,

$C=c_1^{z_1}c_2^{z_2}...c_k^{z_k}$

Let $d = \min\{x_i, y_j, z_h \}$ where $1 \le i \le n, 1\ \le j \le m, 1\le h \le k$ then $$d \le 5$$

PS: I read above one hunded papers, I observed that in any case $\min\{x_i, y_j, z_h \} \le 3$

**Example 1:** Ten solutions of Catalan-Fermat equation

**Example 2:**

$2^4.3^5.7^6+5^9.11^8=19^1.23^1.47^1.6679^1.3051977^1$

**See also:**

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