Mathematical Fallacy 2: Is \(3458=1729\)?

Algebra Level 1

\[\begin{equation} \begin{split} 1729^2=&1729 \cdot 1729 \quad & \ldots (1) \\ 1729^2-1729^2=&1729 \cdot 1729-1729^2 \quad & \ldots (2) \\ (1729+1729)(1729-1729)=& 1729(1729-1729) \quad & \ldots (3) \\ \require{cancel} (1729+1729)\cdot \cancel{0}=&\require{cancel}1729\cdot \cancel{0} \quad & \ldots (4) \\ 3458=&1729 \end{split} \end{equation} \]

The above shows my attempt to prove that \( 3458 = 1729 \). In which of these steps did I make a flaw in my logic?

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