Problem 1. Let the natural numbers $x$ and $y$ be such that the fractions $\frac{7 x-5 y-3}{3 x+9 y-15}$ and $\frac{1}{5}$ are equivalent. Determine the value of the expression $(16 x-17 y)^{2015}$.
## Solution. 1p by default

| The given fractions are equivalent if $\frac{7 x-5 y-3}{3 x+9 y-15}=\frac{1}{5}$ | $\mathbf{1 p}$ |
| :--- | :--- |
| $5(7 x-5 y-3)=3 x+9 y-15$ | $\mathbf{1 p}$ |
| $35 x-25 y-15=3 x+9 y-15$ | $\mathbf{1 p}$ |
| $35 x-25 y=3 x+9 y$ | $\mathbf{1 p}$ |
| $32 x=34 y \Leftrightarrow 16 x=17 y$ | $\mathbf{1 p}$ |
| $(16 x-17 y)^{2015}=0$ | $\mathbf{1 p}$ |