Pierre Elliott Trudeau H.S.


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Welcome to the Pierre Elliott Trudeau H.S. Computer Science Club!

Location

Where: Rooms 220, 222, and 223, Computer Science Wing, Pierre Elliott Trudeau High School.

When: Wednesdays, 3:00 - 4:00 pm.

Resources

Facebook page

Facebook group

Moodle group

Our website

d's Homework

\mathcal{Prove}

\displaystyle \sin(\theta)\ne0,N\in\mathbb{Z}^+\implies\left|\sum_{x=0}^N(\cos(2\theta)+i\sin(2\theta))^x\right|\leq\left|\frac{1}{\sin(\theta)}\right|

\displaystyle N\text{ square-free}\implies x^{\phi(N)+1}\equiv x\pmod N

Square-free and \phi. An example of a consequence is x^5\equiv x\pmod{10}

\displaystyle x=x_x^x\implies x=x_{x_{x_x^x}^{x_x^x}}^{x_{x_x^x}^{x_x^x}}

\displaystyle \sum_{k=0}^N \binom{N}{4k} = \frac{2^N}{4}+\frac{\sqrt{2}^N\times\cos{(45^{\circ}\times N)}}{2}

In this, find a grid where the ball cannot leave within any finite amount of time, or prove that it is impossible to find such a grid.

In this, prove that the number of perfect solutions is always either 0, or a power of 2.


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