Today it is the question 2 of Kyoto University.
Question 2 is the problem about integers. The point of this question is whether you can find that one of the two consecutive interges must be odd and another one must be even. You see that either $n$ or $n+1$ is even.
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Now it is the season of the entrance exams of Japanese Universities.
Each university gives their own exams and I will begin the maths exams of Kyoto University for this year, which is presented on the 25th February 2019. It contains 6 main questions for 150 minutes. Today I will give you the first question; the first one is a bit difficult but the second integrations are very standard. (1) Let $x = \cos \theta$, then $0<x<1$ for $0 < \theta < \frac{\pi}{2}$.
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Assume that \(\tan 1^{\circ}\) is rational. |
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