The Number Theory Of '1'

\[\large1111111 \times 1111111 = \, ? \]

Hint:

\[\begin{array} {rcl} 1 \times 1 & =& 1 \\ 11 \times 11 & = & 121 \\ 111 \times 111 & =& 12321 \\ 1111 \times 1111 & =& 1234321 \end {array} \]

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