Does exsit pure friendship between man and woman?

I don't know the answer, but I can give an example.

Sometimes when I feel tired of replying customers who want to buy solar panels as well as solving their vital and different problems repeatedly, I will gossip with my friends.

Her name is Lucy, an out-going, kind, and beautiful girl. She met a boy when she was young, His name was Peter. When I was in a senior high school, she introduced him to me. At that time, I found Peter loved her but unfortunately she didn't believe that.

So when they graduated, they all worked in Shenzhen, Peter finally professed his love, but she refused him and didn't meet for a long time, 

Nowadays, they also have dates as a friend somtimes. I knew Lucy don't love him but she need someone company her, so does he.

Perhaps we could also discuss this topic of companionship next time. Can someone stay alone forever?