True/False Question :
Let $A$ be a commutative ring with $1$, and let $a,b,c\in A$. Suppose there exist $x,y,z\in A$ such that $ax+by+cz=1.$ Then there exist ${x}',{y}',{z}'\in A$ such that $a^{50}{x}'+b^{20}{y}'+c^{15}{z}'=1$.
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