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Author Archives: incertia
Simon Marais Mathematics Competition 2019
This year’s contest had some interesting problems. I’ll present some example solutions to the less technically challenging of the lot. Problem A1: Let . Define a recursive sequence by letting be the sum of and the product of its distinct … Continue reading
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Complex Numbers are Very Real
A brief while ago I had a discussion with some people who claimed that complex numbers may be very hard to wrap your head around. This is arguably quite true, as intuition can be different for everyone. In this post, … Continue reading
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Cheap Nullstellensatz
I was recently asked to prove a nonexhaustive set of cases for the weak Nullstellensatz, and the proof was so deceptively simple I decided to share it. The main theorem goes along the lines of this. Nullstellensatz: Let be an … Continue reading
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ISL 2017 A1
Problem A1: Let and be positive integers such that If , prove that the polynomial has no positive roots. Solution A1: We appeal to a similar strategy that is used in IMO 20122. Write … Continue reading
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IMO 2018 Day 2
Day 2 had a bunch of really nice problems with more advanced techniques required to solve them. Problem 6 is also hard and I will be writing it up at a later time. Problem 4: A site is any point … Continue reading
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IMO 2018 Day 1
I have solved problems 1 and 2. I have not yet attempted problem 3 but I believe that it is beyond me, especially within a time frame of four and a half hours. Problem 1: Let be the circumcircle of … Continue reading
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I finally released a thing
It’s a small tool to parse Unity3D TestResults files from testing in CI/CD environments, but it’s a tool nevertheless. You can find it at https://hackage.haskell.org/package/unitytestresultparser.
Posted in Programming, Software
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Revenge of the Finite Fields
A few days ago, I posted some proofs and a construction of finite fields. It turns out there are a lot more nice constructions and proofs and problems related to finite fields, so I’ll be sharing some of them here. … Continue reading
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Finite Fields for Mortals
I’ve been studying a bunch of cryptography lately, and I thought it would be nice to present finite fields in some relatively easy to understand way that doesn’t require too much prior knowledge. All that is really needed here is … Continue reading
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UIUCTF2017 – uiuctfsck
This was a brainfuck interpreter that let you print out some internal machine state. Notice that the interpreter does not like it if we have the string “machine” in our format string. We examine the machine object, and notice that … Continue reading
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