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Question Number 1776 by 123456 last updated on 20/Sep/15

P_k ={x∈N,n∈N:x>0,Σ_(n∣x) 1=k}  C=∪_(k≥3) P_k   {0,1}∪C∪P=N  proof or give a counter example that  (x,y,z)∈C^3 ,x^2 ∣yz⇒x∣y∨x∣z

$$\boldsymbol{\mathrm{P}}_{{k}} =\left\{{x}\in\mathbb{N},{n}\in\mathbb{N}:{x}>\mathrm{0},\underset{{n}\mid{x}} {\sum}\mathrm{1}={k}\right\} \\ $$ $$\boldsymbol{\mathrm{C}}=\underset{{k}\geqslant\mathrm{3}} {\cup}\boldsymbol{\mathrm{P}}_{{k}} \\ $$ $$\left\{\mathrm{0},\mathrm{1}\right\}\cup\boldsymbol{\mathrm{C}}\cup\mathbb{P}=\mathbb{N} \\ $$ $$\mathrm{proof}\:\mathrm{or}\:\mathrm{give}\:\mathrm{a}\:\mathrm{counter}\:\mathrm{example}\:\mathrm{that} \\ $$ $$\left({x},{y},{z}\right)\in\boldsymbol{\mathrm{C}}^{\mathrm{3}} ,{x}^{\mathrm{2}} \mid{yz}\Rightarrow{x}\mid{y}\vee{x}\mid{z} \\ $$

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