On the final matchday of the Premier League season, Arsenal secured a 2-0 victory against Brighton and Hove Albion to complete the league double over the Seagulls for the first time in over 40 years. With the win, they leapfrogged Everton to finish eighth, just a point and place behind London rivals Tottenham Hotspur.Although Arsenal dominated the first half, they opened the scoring only after the break thanks to a brilliant goal from Nicolas Pepe, who added a second 11 minutes later to give the Gunners a comfortable advantage.Brighton, on the other hand, lacked fluency going forward. The Seagulls attempted only five shots throughout the whole match, with just one on target.The result means Arsenal have won five successive Premier League games under Mikel Arteta for the first time. On that note, here are five talking points from the match at the Emirates Stadium.#1 Arsenal have a busy summer ahead of themDavid Luiz will leave Arsenal this summerIn addition to David Luiz, a number of first-team players could be on their way out of the club this summer. According to reports, Dani Ceballos' loan spell with the Gunners will not be extended and he will return to Real Madrid.Meanwhile, Willian, who only joined last summer, could also be shown the door. The Arsenal winger has made 25 appearances this season but scored just once and provided five assists.The Brazil international was left out of the matchday squad against Brighton due to an apparent calf injury and it looks as though Willian has played his final game for the north London club.Dani Ceballos will leave Arsenal after his loan spell, he’ll be one of the many players leaving the club. There’s no chance to stay - he’s coming back to Spain. 🇪🇸 #AFCReal Madrid are open to sell him on a permanent deal this summer, waiting for new proposals. ⏳⚪️— Fabrizio Romano (@FabrizioRomano) May 22, 2021There is also speculation over the futures of Hector Bellerin and Alexandre Lacazette, who could both depart Arsenal. Given the club's dismal season, it is evident that there is plenty of work to do this summer.#2 Nicolas Pepe is finally beginning to prove his worthNicolas Pepe celebrates his first goalWith nine goals in his last 13 Premier League starts, Nicolas Pepe is beginning to live up to his £72 million price tag. The Ivory Coast international arrived in August 2019 but in his first season with Arsenal, Pepe scored just five times in 31 Premier League appearances.Against Brighton and Hove Albion, the 25-year-old netted a brace to take his goal tally this season to 16 in all competitions. With superb performances in recent games, Pepe has truly nailed down his spot in the starting XI.Arsenal fans will hope the former Lille midfielder can continue his great scoring form next season and help Arsenal get back into the Champions League.Only Alexandre Lacazette (13) has scored more goals than Nicolas Pépé (10) in the Premier League this season.It's the first time he's scored 10+ goals in the league for Arsenal. pic.twitter.com/lHhg3dYPqG— Squawka Football (@Squawka) May 23, 2021