WASHINGTON (AP) — Ted Cruz stretched matters involving Iran and his own finances. Donald Trump seemed to forget he proposed a massive tax on Chinese goods. Chris Christie took a magic eraser to things he's said and Ben Carson was caught unaware of the punishing ways the Islamic State group says, Thank You for Not Smoking.
The first Republican debate of the new year brought a blizzard of dubious claims and some outright errors.
A look at some claims and how they compare with the facts:

CRUZ: "President Obama's preparing to send $100 billion or more to the Ayatollah Khamenei."
THE FACTS: Cruz makes it sound like the U.S. is bestowing the largest-ever foreign aid payment on longtime foe Iran. The reality is much more ordinary: A seven-nation nuclear deal commits Tehran to curbing its nuclear activities. In exchange, Iran regains access to about $100 billion of its own money that had been frozen under international sanctions.
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TRUMP on Syrian refugees: "When I look at the migration, I looked at the line, I said ... where are the women? It looked like very few women. Very few children. Strong, powerful men, young and people are looking at that and they're saying what's going on?"
THE FACTS: Apparently whatever Trump saw of the refugees wasn't complete. Of the 4.6 million Syrians identified by the U.N. High Commissioner for Refugees as humanitarian "persons of concern," men ages 18 to 59 make up 21.4 percent. The rest are women, children or people age 60 or older.
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JEB BUSH: "We need to move our embassy from Tel Aviv to Jerusalem to send a serious signal that we're back in the game with Israel."
THE FACTS: This political chestnut is the Energizer bunny of political promises, made by candidate after candidate over recent decades. But as long as Israel and the Palestinians remain in conflict over Jerusalem's status, the idea remains an issue in on-again, off-again peace talks and no president has been willing to follow through.
The promise has been made in various forms at least since Bill Clinton adopted it in "principle" in 1992. Congress three years later passed a law calling for the U.S. embassy to be moved to Jerusalem by 1999, but presidents of both parties always have waived the requirement. Bush's brother, George W. Bush, upped the ante when he promised in 2000 to start the move "as soon as I take office," then didn't.
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MARCO RUBIO: "Unfortunately, Gov. Christie has endorsed many of the ideas that Barack Obama supports," including "the appointment of Sonia Sotomayor" to the Supreme Court.
CHRISTIE: "Let's set the facts straight. First of all, I didn't support Sonia."
THE FACTS: Actually, he supported her appointment, despite reservations.
Christie's own statements when he was running for governor of New Jersey in 2009 show that while he wasn't crazy about Sotomayor as a Supreme Court justice, he wasn't dead set against her, either.
"After watching and listening to Judge Sotomayor's performance at the confirmation hearings this week, I am confident that she is qualified for the position," he said, arguing that Obama should be allowed to choose a nominee "who has more than proven her capability, competence and ability," adding, "I support her appointment."
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CARSON on pursuing Islamic State militants wherever they can be found: "Why should we let their people be sitting there smoking their cigars, sitting in their comfortable chairs in Raqqa?"
THE FACTS: Carson is not likely to find IS fighters lounging with cigars in Raqqa, their de facto capital in Syria. The group has imposed a strict smoking ban throughout its territory in Syria and Iraq. In fact, the militant group implements stiff fines for anyone caught smoking, and even more brutal punishments for those caught selling cigarettes, water pipes or anything that can be smoked, cigars included.
Also in the debate, Carson suggested Syrian refugees be allowed to settle in "al-Saqqa province, where they'll be in their own country."
But there is no such place. He probably meant al-Raqqa, or Raqqa. As an IS stronghold, it would not be much of a safe haven for people trying to flee the group.
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CHRISTIE, countering Rubio's criticisms for his past positions: "Common Core has been eliminated in New Jersey." ''I never wrote a check to Planned Parenthood."
THE FACTS: Common Core has not been eliminated in his state — far from it.
A panel Christie put together recommended a series of changes to state standards this week, but only recommended changes to 232 out of 1,427 standards in math and English. The panel also proposed renaming the standards the New Jersey Student Learning Standards. A separate Christie panel recommended the state continue using a Common Core-aligned test — and require it for graduation by 2021.
On Planned Parenthood, Christie's denial is at odds with a Sept. 30, 1994, Newark Star-Ledger story that quotes Christie as saying, "I support Planned Parenthood privately with my personal contribution, and that should be the goal of any such agency, to find private donations."
Christie was running for local office in Morris County, New Jersey, at the time. The same quote appeared again in a book, "Chris Christie: The Inside Story of his Rise to Power," a book with which Christie cooperated.
The original story was written by Star-Ledger reporter Brian Murray, who now works as a spokesman for Christie in the governor's office. On Tuesday, Christie said he was misquoted in the 1994 story.
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TRUMP, denying he told The New York Times he favored a 45 percent tax on Chinese goods: "That's wrong. They were wrong."
THE FACTS: Trump began wriggling out of his idea for a massive tax on Chinese goods soon after he told the paper last week that he would impose one and that "the tax should be 45 percent."
Several days later, he said the tariff could well be much less than that and might not be needed at all because China probably would start trading more fairly in order to avoid it. Now, he denies ever proposing 45 percent, despite his remarks on the record.
More broadly, China no longer appears to be the economic powerhouse portrayed by Trump. Its major stock market has had a rocky start in 2016 and its manufacturing sector began contracting last March as growth slowed, according to a purchasing manager index.
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CRUZ, asked about loans from two large banks totaling as much as $1 million that fueled his 2012 Senate campaign, said he and his wife "ended up investing everything we owned." He acknowledged his failure to disclose the loans to the Federal Election Commission, saying: "Yes I made a paperwork error."
THE FACTS: Cruz did, as he asserted, eventually disclose the loans in personal financial forms filed with the Senate. But citing a mere "paperwork error" in failing to report the loans to the FEC glossed over the fact that the law requires candidates to make such reports to the election regulators.
He also did not address the fact that a large chunk of the loans came from Goldman Sachs, where his wife works as an executive, and whether that might have made the loan possible.
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CRUZ, asked to explain his slam against Trump's "New York values," said, "not a lot of conservatives come out of Manhattan. I'm just sayin'."
THE FACTS: Cruz may dislike New Yorkers, but he's been willing to take a bundle of money from one of them. Wall Street hedge fund mogul Robert Mercer contributed $11 million in April to a Cruz-aligned super PAC, according to federal filings. And there's also that Goldman Sachs loan.
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CRUZ: Any country that makes U.S. service members get on their knees like the 10 sailors whose boats were boarded and seized by the Iranian military this week "will feel the full force and fury of the United States of America."
CHRISTIE: "Tin pot dictators ... are taking our Navy ships."
THE FACTS: Neither candidate addressed the fact that the short-lived crisis was created by the U.S. sailors who steered their boats into sovereign Iranian waters, where they were boarded and seized by Iranian naval forces. Defense Secretary Ash Carter said Thursday that the U.S. sailors had made a navigation error.
Under such circumstances it would not be unusual to disarm members of a foreign military force — even a small one like the two Navy boats — and hold them temporarily for questioning. What was exceptional about this episode — and perhaps a provocation — is that the Iranians videotaped the Americans during the encounter and posted the images on the Internet.
The suggestion by Cruz that he would have launched a military attack on Iran in response to such an incident is hard to square with accepted international tests for the use of force.
Iran returned the sailors unharmed and their boats undamaged.
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Associated Press writers Josh Cornfield in Ardmore, Pennsylvania, Jill Colvin in Des Moines, Iowa, and Vivian Salama, Chad Day, Josh Boak, Robert Burns and Matthew Lee in Washington contributed to this report.