This is such a problem here in India, and asking someone for a receipt is often interpreted as a lack of trust. One pompous old gentleman actually collected a significant cash deposit on a land sale from my father 30 years ago and refused to give a receipt, saying
No question of giving receipt, my word is my honour. You can expect the land to be registered into your name within 2 days. If you doubt my integrity, you need not purchase my property.
But I have almost always needed receipts mainly for my own sense of security, so I learned to ask for one in such a way that no mistrust was implied -- most commonly by suggesting that I needed it for my personal or organizational financial records:
Could you please give me a receipt for that Rs.12,500 payment? I need it for my files, you see, when I calculate the annual financial statement.
I need to furnish a receipt to the company to prove for their files that I actually made this purchase in the expected manner...
I need a receipt for my financial records to claim an income tax deduction.
Someone I know would even go so far as to put the blame on his wife:
My wife absolutely insists on collecting and filing receipts to know where the money is disappearing every year!
Now, what is important is not that your whatever reason should be extremely credible, but that by expressing your need for a receipt with sincere goodwill, you do indirectly manage to convey to your friend that you absolutely do not mistrust him, and that allows him to "save face" in the transaction.