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- Jan 26, 2012

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Thanks again to those who participated in last week's POTW! Here's this week's problem!

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Remember to read the POTW submission guidelines to find out how to submit your answers!

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**Problem**: Let $a,b\in\mathbb{Z}$, and let $p\in\mathbb{Z}^+$ be prime. Prove the "freshman's binomial theorem"; i.e. show that $(a+b)^p\equiv a^p+b^p\pmod{p}$.-----

**EDIT**: I overlooked the fact that it isn't true for*all*positive integers (thanks Opalg). I've corrected the statement for this week's problem.Remember to read the POTW submission guidelines to find out how to submit your answers!

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