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

No

The spelling and meaning of "divertem" are identical in both Brazilian and Continental Portuguese. However, there are differences in pronunciation and typical usage:

• Pronunciation: In Brazilian Portuguese, the unstressed vowels are generally more open and audible. In Continental Portuguese, speakers tend to reduce unstressed vowels significantly, often making the "e" in "divertem" sound much shorter or nearly silent.
• Usage (Grammar): While the word itself is the same, the way it is used in a sentence—specifically when used reflexively to mean "to have fun"—differs. Brazilians typically use proclisis (placing the pronoun before the verb: se divertem), whereas the standard usage in Portugal is enclisis (placing the pronoun after the verb: divertem-se).

Brazilian Portuguese Examples

1. As crianças se divertem muito no parque. (The children have a lot of fun in the park.)
2. Essas piadas divertem os alunos. (These jokes entertain the students.)
3. Eles se divertem com os novos jogos. (They have fun with the new games.)
4. As festas de rua sempre divertem a todos. (Street parties always entertain everyone.)
5. Os turistas se divertem com a nossa cultura. (The tourists have fun with our culture.)

Continental Portuguese Examples

1. As crianças divertem-se muito no parque. (The children have a lot of fun in the park.)
2. Estas piadas divertem os alunos. (These jokes entertain the students.)
3. Eles divertem-se com os novos jogos. (They have fun with the new games.)
4. As festas de rua sempre divertem a todos. (Street parties always entertain everyone.)
5. Os turistas divertem-se com a nossa cultura. (The tourists have fun with our culture.)