Problem je riješen.

Je is the 3rd person singular present form of biti (to be), so here it means is.

So:

• Problem = problem
• je = is
• riješen = solved / resolved

Together: Problem je riješen. = The problem is solved / The problem has been solved.

A useful thing to know is that je is a clitic, so it usually appears in second position in the sentence. That is why it comes after Problem.

Because riješen is the form used for a passive/resultative meaning: solved, resolved.

Compare:

• riješio = solved as in he solved
• riješen = solved as in it is solved

So:

• On je riješio problem. = He solved the problem.
• Problem je riješen. = The problem is solved / has been solved.

In other words:

• riješio = active, tied to the person doing the action
• riješen = passive/adjectival participle, tied to the thing affected by the action

This is a passive/resultative construction:

• Problem = subject
• je = form of to be
• riješen = passive participle

It describes the state resulting from a completed action.

So Problem je riješen can mean:

• The problem is solved
• The problem has been solved
• The problem is resolved

In real usage, Croatian often uses this kind of structure where English might choose either a simple passive (is solved) or a present perfect passive (has been solved), depending on context.

Because it has to agree with problem in gender, number, and case.

Problem is:

• masculine
• singular
• nominative

So the participle also appears in the masculine singular nominative form:

• riješen

If the noun changed, the participle would change too:

• Situacija je riješena.
  Situation is feminine singular, so: riješena
• Pitanje je riješeno.
  Question is neuter singular, so: riješeno
• Problemi su riješeni.
  Problems is masculine plural, so: riješeni

It is in the nominative singular.

That is because problem is the subject of the sentence:

• Problem je riješen. = The problem is solved.

Even though English learners may feel this is “passive,” the noun is still the subject, so nominative is exactly what you would expect.

Because Croatian has no articles like English a/an/the.

So problem can mean:

• a problem
• the problem

Which one is intended depends on context.

In this sentence, English will usually translate it as the problem because that sounds most natural:

• Problem je riješen. = The problem is solved / has been solved.

Yes. Very often it can.

Croatian Problem je riješen focuses on the resulting state: the problem stands in a solved condition.

Depending on context, natural English could be:

• The problem is solved.
• The problem has been solved.
• The issue has been resolved.

So if you are translating, choose the English version that fits the situation best.

Yes, Croatian word order is more flexible than English.

The neutral order here is:

• Problem je riješen.

But you may also hear:

• Riješen je problem.

That version is possible, but it sounds more marked and can shift the emphasis. For example, it may highlight the fact that the problem is solved, or sound a bit more formal or stylistic.

One important point: the clitic je still tends to stay in second position, so word order changes have to respect that rule.

A rough English-friendly guide would be:

• ri ≈ ree
• je ≈ yeh
• š = sh
• en ≈ en

So approximately:

• riješen ≈ ree-YEH-shen

A few pronunciation notes:

• rje in Croatian can feel a little compact to English speakers.
• š is always like English sh in ship.
• Stress is not usually marked in normal writing, so beginners often learn pronunciation by listening rather than from spelling alone.

In this sentence, it behaves a lot like an adjective, even though it comes from a verb.

That is why it agrees with the noun:

• riješen (masculine)
• riješena (feminine)
• riješeno (neuter)
• riješeni / riješene / riješena (plural forms)

Because of that, learners often find it helpful to think of it as solved in the sense of an adjective-like participle.

So:

• problem
  • riješen
• literally something like problem + solved

It comes from the verb riješiti, which means to solve, to resolve, to settle.

Examples:

• Riješiti problem = to solve a problem
• On je riješio problem. = He solved the problem.
• Problem je riješen. = The problem is solved / has been solved.

Riješiti is a perfective verb, which fits well with the idea of a completed action and its result.

Yes, depending on context.

In English, natural translations might be:

• The problem is solved.
• The issue is resolved.
• The matter has been settled.

Croatian problem is very close to English problem, but translation should still follow the context, not just the dictionary.

Yes, very common.

This pattern:

• noun + je/su + participle

is extremely common for expressing that something is done, finished, prepared, opened, closed, resolved, and so on.

For example:

• Vrata su zatvorena. = The door is closed / The doors are closed.
• Zadatak je napisan. = The task is written / has been written.
• Problem je riješen. = The problem is solved / has been solved.

So this is a very useful sentence model to learn early.