How did the US solve this issue during every election until now?

Has it been solved?

What does it mean to solve?

You said it was solved or am I missing something? Can't things be continuously improved?

This comment shows exactly why I made the original post. This assumes there is a problem to be solved. The flat out fact is that it hasn't been a problem. The real problem is that politicians say there is an issue with no proof in order to get into grand debates about how to solve the nonexistent problem all the while creating -real- problems of disenfranchising actual legitimate voters when they implement solutions to the nonexistant problem. The orders of magnitude of people denied their rightful ability to vote compared to the fraud in voting are not even funny. Yes, fraud does happen. It is almost never a real issue but programs to 'fix' the fraud are a real problem.

The check for citizenship is not done at the polling place; it's done at the time of voter registration with plenty of accepted IDs.

There are checks such as when registering to vote. They are not rigorous checks because rigorous proof of citizenship has not been needed by most US citizens for most the country's existence, and there is no way to rapidly switch to a rigorous system without disenfranchising a large number of older citizens and poorer citizens.

Registrations of individual registrants can be challenged and then a more detailed examination is done. Both Republican and Democrat local or state parties keep an eye on registrations and challenge any the think are bogus.

Extensive statistical checks after elections by numerous statisticians (and by most major political parties) shows that this system is working fine, so there is no justification for rushing a transition to a more rigorous system. There is time to design a system that will work for all citizens.

We could get a long way there by just grandfathering in everyone who voted in the last 10 years, and making sure there is extensive help going forward for anyone who cannot afford the cost of getting the necessary documents to get the new ID or who cannot get those documents.

that's only true of federal elections, not universally tho.