Has an Olympic Basketball (Men) game ever ended 35-19?
Exactly once. On August 7, 1936, Japan beat China 35-19, and no Olympic Basketball (Men) game before or since has ended that way. When it happened it was a scorigami, the first 35-19 in league history.
That makes 35-19 the 126th most common final score out of 698 that have ever occurred in Olympic Basketball (Men). One point away, 36-19 has happened never and 35-20 has happened never.