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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