A megoldás létezik.

A is the Hungarian definite article, equivalent to English the.

So:

• a megoldás = the solution

Hungarian has two forms of the definite article:

• a before most consonants
• az before vowels

For example:

• a ház = the house
• az alma = the apple

In A megoldás létezik., megoldás starts with a consonant sound, so a is used.

Megoldás means solution.

It comes from the verb megold, which means to solve or to untie/unfasten, depending on context.

A very common Hungarian noun-forming ending is -ás / -és, which often creates an action or result noun from a verb.

So very roughly:

• megold = solve
• megoldás = solving / solution

In this sentence, it means solution in the normal English sense.

Because létezik means exists, while van usually means is / there is / has presence.

So:

• A megoldás létezik. = The solution exists.

This has a stronger sense of actual existence, often in a more formal, abstract, or philosophical way.

Compare:

• Van megoldás. = There is a solution.
• A megoldás létezik. = The solution exists.

Both can be translated similarly in some contexts, but létezik focuses more directly on existence itself.

It is a normal word, but it often sounds a bit more formal, abstract, or emphatic than van.

You might hear létezik in contexts like:

• philosophy
• science
• mathematics
• serious discussion
• emphasizing that something really does exist

For everyday speech, Hungarian often prefers van where English might say exists.

So this sentence is perfectly correct, but depending on context, it may sound slightly more formal or deliberate than a simpler everyday phrasing.

Létezik is:

• third person singular
• present tense
• indefinite conjugation

So it means:

• he/she/it exists
• or here, the solution exists

Hungarian verbs do not need a separate word like it if the subject is already present.

So:

• A megoldás létezik. literally works as
• The solution exists.

Because létezik already means exists as a full verb.

English sometimes needs a structure like there is or it is, but Hungarian often expresses the idea directly with a single verb.

So:

• létezik = exists

There is no need for an extra verb like is.

Not exactly as naturally as Van megoldás.

A megoldás létezik. is specifically The solution exists, with a definite noun phrase: the solution.

If you want the more general idea There is a solution, Hungarian would more naturally say:

• Van megoldás.

That sentence has no article and sounds more like introducing the existence of a solution for the first time.

So the difference is roughly:

• Van megoldás. = There is a solution.
• A megoldás létezik. = The solution exists.

Both are possible, but the emphasis changes.

• A megoldás létezik. is the more neutral order: The solution exists.
• Létezik a megoldás. puts more focus on the fact of existing, something like The solution does exist or There really is the solution depending on context.

Hungarian word order is strongly connected to focus and information structure, not just grammar.

So the given sentence is the straightforward neutral version.

A rough pronunciation guide:

• megoldás ≈ meh-gol-daash
• létezik ≈ lay-teh-zik

A few useful points:

• e is usually like e in bet
• é is a longer sound, roughly like ay in say but pure and without much glide
• á is a long a, roughly like a longer open vowel
• stress in Hungarian is almost always on the first syllable of the word

So:

• ME-gol-dás
• LÉ-te-zik

The accent marks in Hungarian are important: they are not optional.

In this sentence:

• á
• é

usually indicate long vowels, and the vowel quality may also change slightly.

So:

• a and á are different vowels
• e and é are different vowels

You should learn them as part of the spelling of the word, not as decoration.

For example:

• letezik would be misspelled
• the correct form is létezik

You normally would not say Megoldás létezik in standard neutral Hungarian.

If you are talking about a specific solution, you use the definite article:

• A megoldás létezik. = The solution exists.

If you mean a solution exists in a general sense, Hungarian would usually say:

• Van megoldás.

So dropping the article here does not sound like a normal equivalent of English Solution exists.

Yes. A megoldás is the subject, and létezik is the verb.

So the structure is:

• A megoldás = subject
• létezik = verb

This is very similar to English:

• The solution = subject
• exists = verb

Yes, very easily.

Because létezik means exists, the sentence can sound like something from:

• mathematics: a solution exists
• logic
• philosophy
• formal argumentation

In an everyday situation, if someone simply wants to reassure you that a problem can be solved, Hungarian might more naturally say:

• Van megoldás. = There is a solution.

But A megoldás létezik. is absolutely correct and can sound more formal, abstract, or emphatic.