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Donald J. Trump’s language on the campaign trail (“silent majority”) and his divisive tactics (describing Mexican immigrants as “criminals”) seems to draw inspiration from the divide-and-conquer style of Richard M. Nixon.

As it turns out, it was the Nixons who drew inspiration from Mr. Trump – back in 1987, according to a new book.

On Dec. 21 of that year, Mr. Nixon, the former president, dashed off an admiring letter to the real estate developer, according to a new biography of Mr. Trump, “Never Enough,” by Michael D’Antonio.

Pat Nixon, the former first lady, had just caught Mr. Trump’s appearance on Donahue, the daytime talk show, in which Mr. Trump spoke of what ailed America and how to fix it.

“Dear Donald,” Mr. Nixon began, in the previously unpublished correspondence, according to the book. “I did not see the program, but Mrs. Nixon told me you were great.”

“As you can imagine,” he continued, “she is an expert on politics and she predicts that whenever you decide to run for office, you will be a winner!”

The letter is signed, simply, “RMN.”

Donald Trump Likens His Schooling to Military Service in Book A forthcoming biography portrays the presidential candidate, who received draft deferments, as preoccupied by winning and self-promotion since childhood.