The Hollywood Classic cinema in Seoul is popular in a country where 70-year-olds now outnumber people in their 20s.

Xi Jinping gave two cellphones to South Korea’s president, who asked how secure they were. “You can check if there’s a backdoor,” he said with a laugh.

The country’s new president rolled out the red carpet for China’s leader, Xi Jinping, and President Trump this week, but the superpower rivalry is making it harder to balance relations.

Amid skyrocketing demand for artificial intelligence systems, the chip-making giant has been thrust into the economic feud between Beijing and Washington.

At an Asia-Pacific summit, the Chinese leader urged countries to “resist unilateral bullying,” an appeal that seemed at odds with his country’s recent actions.

President Trump traveled to Asia to be a statesman, a showman and a traveling salesman, depending on the audience.

The two leaders reached an agreement on fentanyl, some tariffs and rare earths, at least for a year. But even as the global trade picture cleared a little, Mr. Trump spurred new worries about nuclear proliferation.

By withholding soybean purchases and rare-earth exports, China extracted relief from U.S. tariffs and delayed export controls, without conceding much in return.

Island countries understood that a day like this would come.

It needs the United States for defense and has spent billions building factories in America. But a Trump trade deal this week with China could erase a Korean edge in the U.S. market.

Ahead of a meeting with President Trump, China’s leader signaled that he is committed to competing in manufacturing and technology despite tensions with Washington.

A preliminary tariff deal with President Trump called for a large investment in the United States, while China has warned Seoul not to side with Washington.

President Trump’s visit shows how the United States and China are vying for influence in Asia over trade, technology and the fate of Taiwan.

President Trump is embarking on a six-day diplomatic tour of Asia, testing his role as a statesman and negotiator as he pursues a trade deal with Beijing.

The recent surge in demonstrations by far-right groups presents a challenge for the South Korean government, as it prepares to host both Xi Jinping, the leader of China, and President Trump.

His televised address as prime minister, delivered 50 years to the day after Japan announced its surrender, set a marker for his country’s “deep remorse” over wartime atrocities.