Modulus and Congruences, odd example.

Question

Hey guys I am reading a math book and I got a bit confused on the congruence chapter. I have just seen that $a \pmod n$ = remainder of n|a.
However as an example of " a (mod n) = remainder ", they wrote:

1 = 15 (mod 7)
The peculiar example was: "The integer 29 is 5 mod 6"

Which I understand it would translate as: $$29 = 5 (mod 6)$$ I do know that 29 is congruent to 5 (mod 6), as
$$6 \mid (29-5) = 4 $$ thus, $29 \equiv 5 (mod 6)$.
However 29 is not at all the remainder of $6\mid 5$ so I am confused as to me this example does not make sense (being an example or congruence rather than the remainder). It feels like it is badly written. Please help.

Answer 1

29 is 5 mod 6 means that 29 mod 6 is same as 5 mod 6. When you divide 29 by 6, you get 5 which is same as 5 mod 6. So it is actually 29 mod 6 =5 mod 6, which is in general stated as 29 is 5 mod 6.

Answer 2

The notation is ambiguous. You are parsing it as

$$29 = (5 \text{ mod } 6)$$

but the correct parsing is

$$29 \equiv 5 ~(\text{mod } 6)$$

which is taken to mean the equation is true modulo 6.