| Summary: | In this paper, we find all Lucas numbers written in the form <inline-formula><math display="inline"><semantics><mover><mrow><mi>c</mi><mo>⋯</mo><mi>c</mi><mi>d</mi><mo>⋯</mo><mi>d</mi></mrow><mo>¯</mo></mover></semantics></math></inline-formula>, where <inline-formula><math display="inline"><semantics><mover><mrow><mi>c</mi><mo>⋯</mo><mi>c</mi><mi>d</mi><mo>⋯</mo><mi>d</mi></mrow><mo>¯</mo></mover></semantics></math></inline-formula> is the concatenation of two repdigits in base 10 with <inline-formula><math display="inline"><semantics><mrow><mi>c</mi><mo>,</mo><mi>d</mi><mo>∈</mo><mo>{</mo><mn>0</mn><mo>,</mo><mn>1</mn><mo>,</mo><mo>⋯</mo><mo>,</mo><mn>9</mn><mo>}</mo></mrow></semantics></math></inline-formula>, <inline-formula><math display="inline"><semantics><mrow><mi>c</mi><mo>≠</mo><mi>d</mi></mrow></semantics></math></inline-formula> and <inline-formula><math display="inline"><semantics><mrow><mi>c</mi><mo>></mo><mn>0</mn></mrow></semantics></math></inline-formula>.
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