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By Paul Carsten BEIJING (Reuters) – Apple Inc will boost its investment in China, one of its most important but increasingly difficult markets, and build its first Asia-Pacific research and development center in the country, Chief Executive Tim Cook said on Tuesday. Demand for Apple's phones has plummeted in China, and the government maintains a wary attitude towards foreign technology. Apple's new research and development center will be built by the end of the year, Cook told Vice Premier Zhang Gaoli, one of China's most senior officials, according to the official Chinese state broadcaster.

By Jim Finkle LAS VEGAS (Reuters) – Apple Inc said it plans to offer rewards of up to $200,000 (£152,433) to researchers who find critical security bugs in its products, joining dozens of firms that already offer payments for help uncovering flaws in their products. The maker of iPhones and iPads provided Reuters with details of the plan, which includes some of the biggest bounties offered to date, ahead of unveiling it on Thursday afternoon at the Black Hat cyber security conference in Las Vegas. The program will initially be limited to about two dozen researchers who Apple will invite to help identify hard-to-uncover security bugs in five specific categories.

Apple Inc Chief Executive Tim Cook plans to visit Beijing later this month to meet high-level government officials, at a time when it is facing some setbacks in its most important overseas market, a source familiar with the matter said. Cook has frequently traveled to China since taking the helm of Apple five years ago, but his latest visit comes during a critical period. Last week, billionaire activist investor Carl Icahn said in an interview with cable television network CNBC that he had sold his entire stake in Apple, citing China's economic slowdown and worries about whether the government could make it very difficult for Apple to conduct business.

By Alex Dobuzinskis LOS ANGELES (Reuters) – A cellphone expert overrode the lock function on an Apple iPhone to help Los Angeles police in a homicide investigation around the time U.S. authorities were battling the company to open other phones in criminal cases, court records showed on Thursday. The successful hack of the iPhone 5s in the Los Angeles case is another sign U.S. authorities are turning to third-party contractors to unlock smartphones rather than relying on manufacturers like Apple Inc , which helped in the past. The third-party hacks have Apple racing to strengthen its encryption technology.

By Himank Sharma MUMBAI (Reuters) – India has rejected a plan by Apple Inc to import used iPhones, government officials said on Wednesday, a blow to the U.S. tech giant that has been seeking to revive waning sales of its flagship smartphones. Apple sells what it calls refurbished iPhones at a discount in some countries, including the United States. Extending this practice to India would have likely helped it increase its share in one of the world's fastest growing smartphone markets against competitors with much cheaper offerings.

Apple also said it was raising its capital return program by $50 billion through a $35 billion increase in its share buyback authorization and a 10 percent rise in the quarterly dividend. Apple said it sold 51.2 million iPhones in its second fiscal quarter, down from 61.2 million in the same quarter a year ago but above analysts' estimates of about 50 million devices. Shares of Apple fell 6 percent on heavy volume in after-hours trade, falling below $100 for the first time since February.

U.S. prosecutors said Monday that a “third party” had presented a possible method for opening an encrypted iPhone used by one of the San Bernardino shooters, a development that could bring an abrupt end to the high-stakes legal showdown between the government and Apple Inc. A federal judge in Riverside, California, late Monday agreed to the government's request to postpone a hearing scheduled for Tuesday so that prosecutors could try the newly discovered technique. The Justice Department said it would update the court on April 5. The government had insisted until Monday that it had no way to access the phone used by Rizwan Farook, one of the two killers in the December massacre in San Bernardino, California, except to force Apple to write new software that would disable the password protection.

By Dustin Volz WASHINGTON (Reuters) – The U.S. government and Apple Inc will be able to cross-examine the other's witnesses in a court hearing next week on whether the technology company must help federal investigators unlock an encrypted iPhone tied to one of the San Bernardino killers, Apple said. The hearing, set for Tuesday, is the latest development in a showdown between Apple and the government that has become a lightning rod in the national debate over digital privacy and what kind of data on phones and personal devices should be accessible to law enforcement. All the witnesses have given written declarations in the legal briefs already filed in the case, said an Apple lawyer who spoke to reporters on a conference call on Friday, on condition of anonymity.

The U.S. Justice Department on Thursday said Apple Inc's rhetoric was “false” in a high-profile fight over the government's bid to unlock an encrypted iPhone belonging to one of the San Bernardino shooters. Last month, the Federal Bureau of Investigation obtained a court order requiring Apple to write new software and take other measures to disable passcode protection and allow access to shooter Rizwan Farook's iPhone. Apple has not complied.

By Julia Edwards WASHINGTON (Reuters) – The U.S. Justice Department on Monday sought to overturn a ruling which protects Apple from unlocking an iPhone in a New York drug case. A magistrate judge in Brooklyn last week ruled that the Justice Department could not compel the tech giant to unlock the phone. Prosecutors are relying on the same law in its fight against Apple in a California court, where a judge ordered Apple to unlock an encrypted phone belonging to one of the San Bernardino shooters.