This challenge serves as an introduction to modular arithmetic. As such, the writeup should as well. Let’s check the file.

165 248 94 346 299 73 198 221 313 137 205 87 336 110 186 69 223 213 216 216 177 138 

The description says to take each number mod $37$. If you have not encountered the mod/modulo function before, a simple way to describe it is the remainder. For example, the remainder of $5$ divided by $2$ is $1$. Mathematically, it is written: \[ 5 \equiv 1 \pmod 2 \] …which is read as “$5$ is congruent to $1$ mod $2$”. When there are brackets around the word mod, it means the modulo operation applies to the entire congruence. We say congruent, because $5$ is not equal to $1$, but $5$ and $1$ behave the same under the operation mod $2$.

You may have also used the modulo operator in programming, symbolised by %, e.g. 7 % 3 is $7\mod 3$. So let’s take all these numbers mod $37$. \[ 165 \equiv 17 \pmod {37} \] \[ 248 \equiv 26 \pmod {37} \] \[ 94 \equiv 20 \pmod {37} \] \[ \vdots \]

And so on, you get the idea. Now it wants us to map this to a character set which is the uppercase alphabet, followed by numbers (starting from 0) and then an underscore at the end, starting from 0. So index 0 of the character set goes to A, 1 goes to B, etc.

17 : R
26 : 0
20 : U
13 : N
3  : D
36 : _
13 : N
36 : _
17 : R
26 : 0
20 : U
13 : N
3  : D
36 : _
1  : B
32 : 6
1  : B
28 : 2
31 : 5
31 : 5
29 : 3
27 : 1 

Flag: picoCTF{R0UND_N_R0UND_B6B25531}