Number Theory

We can list out all numbers since there are not that many. 

5 modulo 171 means that the number leaves a remainder of 5 when divided by 171. 

First, we have 5, since we have $171*0 + 5 = 5$

We add 171 to every number from here on. 

So, we have

$5+171=176\\ 176+171 = 347\\ 347+171 = 518\\ 518+171=689\\ 689+171=860\\$

Adding anymore would result in a number greater than 1000. 

Thus, we have $6$ numbers. 

So our answer is 6. 

Thanks! :)