# Multiplication and modulo - Order of operations

Simple question

I have $$a\cdot b\cdot c\;mod\;p$$

How do I interpret this? Do i read it as this $$(abc)\;mod\;p$$ or is it $$a\cdot b\cdot (c\;mod\;p)$$

Or do I completely misunderstand modular arithmetic?

Thanks!

Yes, it's $$(a b c) \mod p$$. In fact $$x \mod p =(x)\mod p \text{ for any expression } x$$

• Oh brilliant explanation by generalising x as any expression – Jamal Rahman Dec 10 '18 at 7:30

You can see this as $$a*b*c(mod p)$$ or $$a(mod\ p) *b(mod\ p)* c(mod\ p)$$.