The Ivorian joined the Côte d'Azur club on a season-long loan and after a slow start, has started to show some of the promise Arsenal splashed £72million on in 2019.
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Pepe opened the scoring in the 15th minute, firing low past Montpellier goalkeeper Jonas Omlin.
His second came rather fortuitously 11-minutes after the interval when his effort took a bobble and a deflection before finding the bottom corner.
The 27-year-old appears at home at the Allianz Riviera having netted eight times in 22 games across all competitions.
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Pepe's brace has taken him joint top in the scoring charts for Nice with six goals alongside former Wigan striker Andy Delort who also got himself on the scoresheet on Wednesday.
Delort joined the Latics in 2014 spending one solitary season at the club before a loan switch to French side Tours a year later.
He played just 11 times for Wigan but failed to score in any of his appearances. Shortly after his departure, the Algerian admitted he struggled to adapt to life in England.
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Meanwhile, former Everton and Chelsea midfielder Ross Barkley came off the bench to net two quickfire goals in the rout.
Barkley replaced Aaron Ramsey in the 67th minute and quickly made an impact on the game, firing his first goal eight-minutes from time.
The 29-year-old was in the right place at the right time to add a second from close range three-minutes later.
The England international is up to three goals for the season following his stunning strike against Rennes on January 2, to open his account for Les Aiglons.
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Nice are owned by INEOS boss, Sir Jim Ratcliffe who showed an interest in buying both Chelsea and Manchester United last year.
Ratcliffe is Britain most-wealthiest man and has led Nice's ambitious project since taking over the club in 2019
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