Size in NT
Using size as a way to handle number theory conditions, for example taking sufficiently large primes. On the border between olympiad algebra and olympiad number theory.
Content
Size in NT is a unit on a very general type of problems that are very frequently seen in olympiads. It usually involves problems which are nominally number theoretic equalities, but for which you'll have to resort to some inequalities.
A lot of the times the inequalities are a bit dumb (like $n \ge 1$ or $m \mid n \implies m \le n$). You also will see a lot of really useful and common techniques such as taking a really big prime $p$, bounding between $2$ squares, proving that a certain function grows faster than other function, taking the maximal element, proving that a sequence of positive integers is decreasing so eventually it must be constant.
Notable Problems
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Taiwan Quiz 2014/3J/5: beautiful problem, a really good example of one of the techniques just mentioned.
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TSTST 2011/8: this walkthrough problem is a great example of using size arguments to prove that a sequence is eventually constant by showing first that it must take finitely many values through bounding and then showing that the sequence is eventually periodic.
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RMM 2020/2: one of the more challenging but really fun problems from the unit.
Recommendations
This is a very important unit that anyone without a really strong background in NT should try. It's an average D difficulty unit, being pretty similar in this regard with the NT construct unit which I recommend taking next. If you haven't done it already I recommend trying the Euclid unit first, which is closely related and a bit easier than this one.