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October 1, 2014

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In this May 3, 2012, photo, Stephen Colbert, host of the “Colbert Report” on Comedy Central, has a laugh onstage with host David Letterman on the set of “The Late Show With David Letterman.”

John Paul Filo / CBS / AP

In this May 3, 2012, photo, Stephen Colbert, host of the “Colbert Report” on Comedy Central, has a laugh onstage with host David Letterman on the set of “The Late Show With David Letterman.”