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Last summer, Celtics forward Jayson Tatum and 76ers center Joel Embiid spent a good deal of time working out together. They work with the same skills trainer, Drew Hanlen, and they have become friends through this connection.

The workouts were intense, and of course they included some ribbing.

“I just kept reminding him that we almost swept them,” Tatum said. “We should have swept them, but we let them win one game.”

Tatum was referring to the Eastern Conference semifinals matchup between their teams, which the Celtics won in a five-game series that was more competitive than a typical five-game series.

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Now that LeBron James has left the Cavaliers and joined the Lakers, there is an opening in the East — for the first time in eight years — for a team without James to seize control of the conference. And the Celtics and 76ers, with their talent, youth, and future assets, are the two that are best positioned to do that.

It is appropriate, then, that they will open the NBA regular season playing against each other on national television on Tuesday night.

“We won [last year’s series], so they are probably a little more fired up or angry than we are,” Tatum said. “But we’re excited to play. We had a lot of good matchups with them last year, a lot of great battles, especially in the playoffs. We’re excited. They’re excited.”

Related: Answers to all of your Celtics questions

The teams have changed very little since last season, particularly in the areas that matter most. The biggest difference for the Celtics is that they now have Gordon Hayward back, not to mention Kyrie Irving, who missed last season’s playoffs series. The biggest difference for the 76ers is that Markelle Fultz, the No. 1 overall pick of the 2017 draft, now appears ready to take on a meaningful role.

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Fultz’s rookie year was mostly a lost season. He battled a shoulder injury as well as a loss of confidence, as his comfort taking shots beyond six feet mysteriously disappeared. But the 76ers insist this was a big summer for Fultz, and sure enough, he will be in the starting lineup on Tuesday night while the NBA world eagerly waits to see what has changed.

“He’s a guy that is very quick, has the ability to get to the basket and pass the ball,” Celtics center Al Horford said. “We know he’s very talented and he’s good to go for them. We’re preparing for him just like all the other guys.”

These teams will meet three more times this season, and neither will read too deeply into Tuesday’s result. Nevertheless, it will be the first chance for both of them to enter this LeBron-free world, the first chance to stake a claim.

Related: Gary Washburn previews the 2018-19 NBA season

76ers at a glance

(Statistics from 2017-18 season)

■  When, where: Tuesday, 8 p.m., TD Garden

■  TV, radio: TNT, WBZ-FM (98.5)

■  Scoring: Joel Embiid 22.9, J.J. Redick 17.1, Ben Simmons 15.8

■  Rebounding: Embiid 11.0, Simmons 8.1, Dario Saric 6.7

■  Assists: Simmons 8.2, T.J. McConnell 4.0, Markelle Fultz 3.8

■  Head to head: The Celtics won the regular-season series last year, 3-1. Boston defeated Philadelphia, 4-1, in the Eastern Conference semifinals.

■  Miscellany: The Celtics averaged 18 turnovers per game against the Sixers last season, their highest against any opponent . . . Boston allowed 95.3 points per game against Philadelphia during the regular season, the fourth lowest among all regular-season foes . . . Philly’s Ben Simmons beat out Boston’s Jayson Tatum and Utah Jazz F Donovan Mitchell for 2018 Rookie of the Year.

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Adam Himmelsbach can be reached at adam.himmelsbach@globe.com. Follow him on Twitter @adamhimmelsbach.