Im a high school student attempting to do this and would like some ideas for the following problem. Im completely stuck in the blind and have no.idea how to proceed. Thanks. Edit: Im so sorry the paper i picked it from had a typo Ive corrected it now and it was rather easy to prove. The first 2 terms had been switched around.
Consider the following sequence where $$ y_{1}=1, y_{2}=2018$$ and $$y_{k+1}=2018y_k + 2019y_{k-1}$$ for $k\ge 2$ Show that there must exist a term in the sequence divisible by $2018^ {2018}$
it is easy to prove that $$y_k=\frac{2019^k-4074341 (-1)^k}{2020}$$ and this will help you