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Ohio State coach Urban Meyer and San Francisco 49ers quarterback Alex Smith can't agree on who will win their celebrity golfing showdown later this month in the 23rd annual American Century Championship at Lake Tahoe.

But the former Utah football coach and Utah quarterback are on the same page when it comes to the Utah-BYU rivalry, which could end after the Utes and Cougars meet on Sept. 15 in Salt Lake City.

"To me, that's a major mistake," Meyer said.

Added Smith: "Same thing as coach said ... It is weird enough that the game is not at the end of the season anymore ... to not play at all would be a mistake."

BYU coaches and players said at their media day last week that they want the series to continue. But Utah athletic director Chris Hill and football coach Kyle Whittingham have both said playing BYU annually might not work any more for the Utes now that they are in the Pac-12.

Meyer said he generally favors the direction college football has taken the past few years, but doesn't like it when longtime rivalries such as Texas-Texas A&M and BYU-Utah are threatened by conference realignment.

"When those things get taken away, I don't like it," he said.

Meyer was 2-0 against BYU during his stint at Utah, beating the Cougars 3-0 in Provo in 2003 and 52-21 at Rice-Eccles Stadium in 2004. Smith was the starting quarterback in both games.

"As close as those schools are, you have to play that game," Smith said, recalling how teammates and alumni quickly made him aware of the rivalry's importance when he arrived as a freshman from the San Diego area.

It will be the first appearance at the July 20-22 tournament at Edgewood Golf Club for both men. Both are being given 40-to-1 odds to win by Harrah's.

But both said they are more concerned with beating the other in their joint teleconference appearance on Thursday.

"It's an opportunity to get another W ... I think I can take him," said Smith, who was on his high school golf team for four years but hasn't played a lot recently due to the birth of a child a year ago.

Meyer said he carries a 12 or 13 handicap and is 1-0 against Smith, having defeated his quarterback in a match in Utah. He said he played more golf during his two years in Utah than he has in the rest of his career put together, talking about playing "every morning" in June and July.

"I just don't want to embarrass myself," he said.

Twitter: @drewjay