Genetic tests have solved one of the enduring mysteries of presidential history and offer insights into the secret life of America’s 29th president.

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WASHINGTON — She was denounced as a “degenerate” and a “pervert,” accused of lying for money and shamed for waging a “diabolical” campaign of falsehoods against the president’s family that tore away at his legacy.

Long before Lucy Mercer, Kay Summersby or Monica Lewinsky, there was Nan Britton, who scandalized a nation with stories of carnal adventures in a White House coat closet and endured a ferocious backlash for publicly claiming that she bore the love child of President Warren G. Harding.

Now nearly a century later, according to genealogists, genetic tests confirm for the first time that Britton’s daughter, Elizabeth Ann Blaesing, was indeed Harding’s biological child. The tests have solved one of the enduring mysteries of presidential history and offer insights into the secret life of America’s 29th president.

At the least, they demonstrate how the march of technology is increasingly rewriting history books.

The revelation has also roiled two families that have circled each other warily for 90 years, struggling with issues of rumor, truth and fidelity. Even now, members of the Harding family remain divided, with some still skeptical after a lifetime of denial and unhappy about cousins who chose to pursue the question. Some descendants of Britton remain resentful it has taken this long for evidence to come out and for her credibility to be validated.

“It’s sort of Shakespearean and operatic,” said Peter Harding, a grandnephew of the president and one of those who instigated the DNA testing that confirmed the relationship to Britton’s offspring.

The Nan Britton affair was the sensation of its age, a product of the jazz-playing, gin-soaked Roaring Twenties and a pivotal moment in the evolution of the modern White House. It was not the first time a president had been accused of an extracurricular love life, but never before had a self-proclaimed presidential mistress gone public with a popular tell-all book.

While some historians dismissed Britton’s account, it remained part of popular lore. HBO’s “Boardwalk Empire” made it a subplot a few years ago. The Library of Congress effectively recalled it last year when it released Harding’s love letters with another mistress, Carrie Phillips.

Britton, 31 years younger than Harding, had a harder time proving her relationship when she revealed it after his death because she had destroyed her own letters with him at his request and because his family insisted he was sterile.

Peter Harding said that, as a boy growing up, he believed the family line.

“My father said this couldn’t have happened because President Harding had mumps as a kid and was infertile and the family really vilified Nan Britton,” said Harding, now 72 and a physician in Big Sur, Calif.

After finding Britton’s book, “The President’s Daughter,” among his father’s belongings, though, he concluded that the man described in it resembled the writer of the letters to Phillips, an expressive romantic who doted on women.

Peter Harding and his cousin, Abigail Harding, decided to pursue the matter and made contact with James Blaesing, a grandson of Britton and son of the daughter she claimed to have conceived with the president. Testing by Ancestry.com, the genealogical website, found that Blaesing was a second cousin to Peter and Abigail Harding, meaning that Elizabeth Ann Blaesing had to have been the president’s daughter.

“We’re looking at the genetic scene to see if Warren Harding and Nan Britton had a baby together, and all these signs are pointing to yes,” said Stephen Baloglu, an executive at Ancestry.com. “The technology that we’re using is at a level of specificity that there’s no need to do more DNA testing. This is the definitive answer.”

The testing also found that Harding had no ancestors from sub-Saharan Africa, answering another question that has intrigued historians. When Harding ran for president in 1920, segregationist opponents claimed he had “black blood.”