Task 1. The distance between telephone poles on a street 1600 m long was 80 m. Due to a certain need, they were rearranged so that the new distance between the poles is 50 m. How many poles remained in the same place after the rearrangement?
Solution. Since $\operatorname{LCM}(80,50)=400$, we get that the unexchanged poles will be those at the first position and every $400 \mathrm{~m}$. Therefore, the total number of unexchanged poles will be $1+1600: 400=5$.