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# Category Archives: Algebra

## Nested radicals

I was trying to solve an olympiad type problem involving a nested radical of the form [tex] \sqrt{a+b\sqrt{r}}.[/tex] I had managed to discover that [tex] \sqrt{a^2- b^2r} [/tex] is an integer but it turned out the trick is to rewrite … Continue reading

Posted in Algebra, Number Theory
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## Polynomial Puzzle and Lill’s Method

I have in mind a polynomial with nonnegative integer coefficients. Can you determine completely the polynomial by just asking two questions? I forgot where I saw this from but it was interesting enough to spur a few lunch time discussions … Continue reading

Posted in Algebra, Geometry/Topology, Problems
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## Magic formula

Was grading some student work and noticed that when they are supposed to solve for [tex] \left(\frac{5y}{4}-\frac{1}{2}\right)^2 +\frac{1}{16} = 1[/tex], 10 out of 16 students expanded the above into a quadratic equation and then used the quadratic formula to get … Continue reading

Posted in Algebra, Teaching
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## Simple algebra*

In the midst of grading exams now. One problem consists of computing determinants and many students give the answer [tex] (1+a)^3 -3a -1 [/tex] without simplifying it to [tex] a^3+3a^2 [/tex]. I have this nagging suspicion that they are not … Continue reading

Posted in Algebra, Linear Algebra, Teaching
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## Prisoner of Benda

is an episode of Futurama where an actual theorem on permutations appear. Although I adore the Simpsons, I’m not much of a Futurama fan. This link explains the theorem and contains the screencap.

Posted in Algebra, Fun Stuff
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