Is the word problema the same in Brazilian and European Portuguese?

Yes

The word "problema" is identical in spelling, meaning, and grammatical gender (masculine) in both Brazilian and Continental Portuguese. The only difference lies in pronunciation.

In Brazilian Portuguese, the pronunciation tends to be more open and "musical," with more distinct, clear vowels. In Continental Portuguese, the pronunciation is more "stress-timed," meaning unstressed vowels are often reduced or almost swallowed, making the word sound more clipped and the rhythm more rapid.

Brazilian Portuguese Examples

1. "Não tem problema, eu te ajudo." (No problem, I'll help you.)
2. "Estamos com um problema no computador." (We are having a problem with the computer.)
3. "Isso não é um problema para mim." (That is not a problem for me.)
4. "Qual é o problema com isso?" (What is the problem with that?)
5. "Ele está criando um problema enorme." (He is creating a huge problem.)

Continental Portuguese Examples

1. "Não há problema, ajudo-te." (No problem, I'll help you.)
2. "Estamos com um problema no computador." (We are having a problem with the computer.)
3. "Isso não é um problema para mim." (That is not a problem for me.)
4. "Qual é o problema com isto?" (What is the problem with this?)
5. "Ele está a criar um problema enorme." (He is creating a huge problem.)