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- Jan 26, 2012
- 995
Thanks again to those who participated in last week's POTW! Here's this week's problem!
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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 $(a+b)^p\equiv a^p+b^p\pmod{p}$.
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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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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 $(a+b)^p\equiv a^p+b^p\pmod{p}$.
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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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