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On 12 June 2017, Silva moved to Italian Serie A side A.C. Milan on a five-year contract for a fee of €38 million with the additional €2 million depending on objectives. Upon signing, he told the press: I’m very happy to have joined such a prestigious club with such a great history.” He was given the number 9 shirt, previously worn by Gianluca Lapadula. Silva made his debut for the club on 27 July, playing 24 minutes in the 1–0 win against CS Universitatea Craiova for the third qualifying round of the UEFA Europa League. On 17 August, for the same competition but in the play-off round, he contributed with two goals and one assist to a 6–0 home routing of KF Shkëndija; on 14 September, already in the group stage, he scored a hat-trick to help the visitors defeat FK Austria Wien 5–1 – in the process, he became the first player to achieve the feat for Milan in Europe since Kaká in 2006, and he was included in UEFA’s Europa League Team of the Week due to his performance. Silva scored his maiden goal in the Italian top flight on 11 March 2018, from a last-minute header in the 1–0 away win over Genoa CFC.
Silva represented Portugal at every youth level. He participated with the under-20 team at the 2015 FIFA World Cup, scoring four goals in the group stage as the nation reached the quarter-finals; previously, at the 2014 UEFA European Under-19 Championship, he became the first player ever to net four times in a single match (6–1 group stage defeat of Hungary), in an eventual runner-up finish for the under-19s. On 8 September 2015, in his first appearance with the under-21 side, Silva scored a hat-trick in 19 minutes (both halves combined), contributing to a 6–1 win against Albania for the 2017 European Under-21 Championship qualifiers. He was called up for the first time to the senior team by head coach Fernando Santos the following 26 August, playing the second half of a 5–0 friendly win over Gibraltar in Porto on 1 September. Silva scored his first goal with Portugal’s main squad on 7 October 2016, featuring the entire 6–0 defeat of Andorra for the 2018 FIFA World Cup qualifiers. Three days later, for the same competition, he netted three times in the first half of an eventual 6–0 triumph in the Faroe Islands. Silva was selected for the 2017 FIFA Confederations Cup, making his tournament debut when he replaced Ricardo Quaresma for the last eight minutes of the 2–2 group stage draw against Mexico. He scored his first goal in the competition on 24 June, playing the full 90 minutes in the 4–0 defeat of New Zealand. In the third-place play-off, in which his team eventually defeated Mexico 2–1 after extra time, he had his early penalty saved by Guillermo Ochoa. In May 2018, Silva was named in Portugal’s final squad for the upcoming edition of the FIFA World Cup, also to be held in Russia. Late into that month, he scored the 1000th goal in the national team’s history during the first half of a friendly with Tunisia in Braga. He made his debut in the competition on 15 June, replacing Gonçalo Guedes in the 80th minute of the 3–3 group stage draw against Spain.