His silver medal over 50 km was the only medal won by a Soviet male skier at the 1968 Olympics, as his 4×10 km team placed fourth.

In the 4×10 km event Vedenin ran the last leg and won by 10 seconds, despite starting with a one-minute lag from Norway.

[4] His gold in the 30 km was the first individual win for a Soviet male skier at the Winter Olympics.

After retiring from competitions he coached skiers at Dynamo Moscow, for which he competed through his entire career.

[4] Since 1989 a competition "Vedenin's Ski Track" («Лыжня Веденина») is held yearly in Dubna, Dubensky District, in his honor.