Interpreting modulus formula $a\cdot b+c\cdot d\equiv 1\mod (bd)$

I'm studying for my final right now, and I came across this equation in my notes

$$(−11)\cdot47 + 14\cdot37 \equiv 1\mod (37\cdot 47)$$

Its been so long since i have seen something like this and i'm not sure if I am interpreting it right. I tried looking it up but couldnt find anything on it.

Does it mean $14\cdot 37\equiv1 \mod 47$ and $-11\cdot 47\equiv1 \mod 37$ and does it work like that for all equations in this formula?

• Yes, your congruences are correct, and this also work in general. – Peter Dec 7 '17 at 17:00
• In the context of modular arithmetic, $a\equiv b\pmod{n}$ if and only if $a-b$ is a multiple of $n$ if and only if there exists some integer $k$ such that $a-b=kn$. One should never write $\equiv$ without a $\pmod{n}$ at the end specifying which specific modular equivalence we are referring to. – JMoravitz Dec 7 '17 at 17:00
• I hope this is the intent of the question! – Peter Dec 7 '17 at 17:08
• Yes this helped! I didn't have mod 37⋅47 written down but that makes more sense. Thank you for your help – Jeg Dec 7 '17 at 17:14