$
abc|{a^2}c + a{b^2} + b{c^2},{b^2}c + a{c^2} + {a^2}b \\
a = \prod\limits_i {p_i^{{a_i}}} ,b = \prod\limits_i {p_i^{{b_i}}} ,c = \prod\limits_i {p_i^{{c_i}}} \\
\prod\limits_i {p_i^{{a_i} + {b_i} + {c_i}}} |\prod\limits_i {p_i^{2{a_i} + {c_i}}} + \prod\limits_i {p_i^{{a_i} + 2{b_i}}} + \prod\limits_i {p_i^{{b_i} + 2{c_i}}} ,\prod\limits_i {p_i^{{a_i} + 2{c_i}}} + \prod\limits_i {p_i^{2{a_i} + {b_i}}} + \prod\limits_i {p_i^{2{b_i} + {c_i}}} \\
\forall k,p_k^{{a_k} + {b_k} + {c_k}}|\prod\limits_i {p_i^{2{a_i} + {c_i}}} + \prod\limits_i {p_i^{{a_i} + 2{b_i}}} + \prod\limits_i {p_i^{{b_i} + 2{c_i}}} ,\prod\limits_i {p_i^{{a_i} + 2{c_i}}} + \prod\limits_i {p_i^{2{a_i} + {b_i}}} + \prod\limits_i {p_i^{2{b_i} + {c_i}}} \\
{a_k} \le {b_k} \le {c_k} \\
p_k^{{a_k} + {b_k} + {c_k}}|\prod\limits_i {p_i^{{a_i} + 2{c_i}}} + \prod\limits_i {p_i^{2{a_i} + {b_i}}} + \prod\limits_i {p_i^{2{b_i} + {c_i}}} \Rightarrow p_k^{{a_k} + {b_k} + {c_k}}|\prod\limits_i {p_i^{2{a_i} + {b_i}}} \Rightarrow {c_k} \le {a_k} \\
{a_k} \le {c_k} \le {b_k} \\
p_k^{{a_k} + {b_k} + {c_k}}|\prod\limits_i {p_i^{2{a_i} + {c_i}}} + \prod\limits_i {p_i^{{a_i} + 2{b_i}}} + \prod\limits_i {p_i^{{b_i} + 2{c_i}}} \Rightarrow p_k^{{a_k} + {b_k} + {c_k}}|\prod\limits_i {p_i^{2{a_i} + {c_i}}} \Rightarrow {b_k} \le {a_k} \\
{b_k} \le {a_k} \le {c_k} \\
p_k^{{a_k} + {b_k} + {c_k}}|\prod\limits_i {p_i^{2{a_i} + {c_i}}} + \prod\limits_i {p_i^{{a_i} + 2{b_i}}} + \prod\limits_i {p_i^{{b_i} + 2{c_i}}} \Rightarrow p_k^{{a_k} + {b_k} + {c_k}}|\prod\limits_i {p_i^{{a_i} + 2{b_i}}} \Rightarrow {c_k} \le {b_k} \\
{b_k} \le {c_k} \le {a_k} \\
p_k^{{a_k} + {b_k} + {c_k}}|\prod\limits_i {p_i^{{a_i} + 2{c_i}}} + \prod\limits_i {p_i^{2{a_i} + {b_i}}} + \prod\limits_i {p_i^{2{b_i} + {c_i}}} \Rightarrow p_k^{{a_k} + {b_k} + {c_k}}|\prod\limits_i {p_i^{2{b_i} + {c_i}}} \Rightarrow {a_k} \le {b_k} \\
{c_k} \le {a_k} \le {b_k} \\
p_k^{{a_k} + {b_k} + {c_k}}|\prod\limits_i {p_i^{{a_i} + 2{c_i}}} + \prod\limits_i {p_i^{2{a_i} + {b_i}}} + \prod\limits_i {p_i^{2{b_i} + {c_i}}} \Rightarrow p_k^{{a_k} + {b_k} + {c_k}}|\prod\limits_i {p_i^{{a_i} + 2{c_i}}} \Rightarrow {b_k} \le {c_k} \\
{c_k} \le {b_k} \le {a_k} \\
p_k^{{a_k} + {b_k} + {c_k}}|\prod\limits_i {p_i^{2{a_i} + {c_i}}} + \prod\limits_i {p_i^{{a_i} + 2{b_i}}} + \prod\limits_i {p_i^{{b_i} + 2{c_i}}} \Rightarrow p_k^{{a_k} + {b_k} + {c_k}}|\prod\limits_i {p_i^{{b_i} + 2{c_i}}} \Rightarrow {a_k} \le {c_k} \\
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