TOKYO — How do you solve a problem like North Korea? It’s a problem that has befuddled American presidents for decades.

Well, Donald Trump, has a new idea. In the first debate Monday night, the Republican candidate appeared to suggest that China should invade North Korea.

“You look at North Korea, we're doing nothing there,” Trump said when asked about his policy on nuclear weapons during the debate. “China should solve that problem for us. China should go into North Korea. China is totally powerful as it relates to North Korea.”

China responded within hours to Trump's suggestion by saying it has been making "unremitting efforts with all sides concerned" to resolve the nuclear issue, according to Foreign Ministry spokesman Geng Shuang on Tuesday.

The idea that China — once North Korea’s patron, now the closest thing it has to a friend (and it’s not that close) — has leverage over North Korea is not new.

Pyongyang’s nuclear tests are routinely met with condemnation then sanctions through the United Nations that are aimed at cutting off the regime’s ability to get parts for its weapons program or earn the money needed to finance it. After this month’s nuclear test, there were many calls for China to get serious about imposing international sanctions on the North.

The sanctions are not effective unless Beijing fully implements them, cracking down on the Chinese intermediaries that do business with North Korea.

Beijing has become increasingly angry during the reign of North Korean leader Kim Jong Un and has supported increasingly stringent sanctions, but analysts say its ultimate consideration has not changed: It does not want the regime to collapse, sending millions of hungry North Koreans into China and, potentially, the 28,000 American troops stationed in South Korea right up to its border.

But Trump’s suggestion that China “go into” North Korea took the exhortations for Beijing to act to a whole new level and is a bit of contrast to his own suggestions over the summer. Remember that back in June, Trump suggested he would deal with North Korea by inviting Kim to Washington — but not for a state dinner, just for hamburgers around a conference table.

On Twitter, there was widespread disbelief at the idea that a military invasion was the answer.

Indeed, analysts poured cold water on the very idea that leaning on China was a new strategy.

“Has the Bush administration not tried to use Chinese leverage to control Pyongyang? Has not the Obama administration?” Eom Sang-yoon, a research fellow at the Sejong Institute told the NK News website.

What Trump "is saying is very basic, so far he has not provided any details on how his policy will be different from that of Obama,” Sang-yoon said.

But the Republican candidate did not just stop at China. He criticized the Obama administration’s nuclear agreement with Iran as “the worst deal I think I've ever seen negotiated.”

Cracking down on North Korea should have been made part of that deal, Trump said.

“Iran is one of their biggest trading partners. Iran has power over North Korea,” Trump said. “When they made that horrible deal with Iran, they should have included the fact that they do something with respect to North Korea.''

That claim had Iran experts scratching their heads

Trump also took the opportunity to again insist that Japan and South Korea — both American allies — should be paying more for their defense.

“Just to go down the list, we defend Japan, we defend Germany, we defend South Korea, we defend Saudi Arabia, we defend countries. They do not pay us,” he said.

“But they should be paying us, because we are providing tremendous service, and we're losing a fortune,” saying that “we are losing billions and billions of dollars.”

“This isn't 40 years ago where we could do what we're doing. We can't defend Japan, a behemoth, selling us cars by the million,” he said.

In fact, these countries do pay for their own defense. Japan pays almost $2 billion a year to host American troops on its soil, while South Korea pays about $850 million annually. We wrote about the costs and benefits of the two alliances earlier this year here.

This is how one former Republican spokesman on the Hill responded:

In Seoul, the government broke with normal diplomatic protocol to rebut Trump’s remarks.

"Our government normally considers it inappropriate to comment on remarks by a particular [American] presidential candidate," Cho June-hyuck, spokesman at the Foreign Ministry, said at a press briefing.

"Nevertheless ... I can say that our government has contributed to and played a role in maintaining and strengthening the combined defense capability of South Korea and the U.S. as well as stably stationing U.S. Forces Korea here," the spokesman said, according to a report from the Yonhap News Agency.

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