Nós temos o mesmo problema.

Portuguese is a pro-drop language, which means the subject pronoun can be omitted because the verb ending already shows the person. Saying Temos o mesmo problema is perfectly correct and more common in everyday speech. Including nós adds emphasis or clarity—especially in writing or when distinguishing “we” from “they.”

Temos is the first‐person plural of ter, which literally means “to have.” It does not mean “to be.” So Nós temos o mesmo problema translates as “We have the same problem,” not “We are the same problem.” If you need “we are,” you would use nós somos or nós estamos depending on context.

In Portuguese, singular countable nouns usually require a definite article. O mesmo problema is “the same problem.” Omitting the article (temos mesmo problema) sounds odd or ungrammatical in Portuguese. You could drop the article in very colloquial or headline-style Portuguese, but it isn’t standard.

Most Portuguese nouns ending in -a are feminine, but there are important exceptions—many of them borrowed from Greek (like problema, sistema, tema). These words are masculine. That’s why we say o problema and o mesmo problema.

Mesmo means “same” or “very.” When you put it before a noun preceded by the article, o mesmo problema, it means “the same problem.” If you place mesmo after the noun (e.g., o problema mesmo), it acts more like an intensifier: “the exact problem,” “that very problem,” often with extra stress or in spoken, informal contexts.

You can add exatamente or justamente:
– Temos exatamente o mesmo problema.
– Nós temos justamente o mesmo problema.
Both convey “the very same problem” with more emphasis.

Make both noun and adjective plural. Also adjust the article:
– (Nós) temos os mesmos problemas.
Here os is the plural masculine article, mesmos agrees in gender and number, and problemas is plural.