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If you are a resident for tax purposes - you will be taxed on all worldwide income (regardless of its source).
If you are a non-resident for tax purposes - you may be taxed only on income from US sources.
Please see for reference IRS publication 519 - http://www.irs.gov/pub/irs-pdf/p519.pdf for rules to determine if you are Nonresident Alien or Resident Alien
You may not use the section 1031 if the condo is your personal property.
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