Vincen wrote:[x] is the greatest integer less than or equal to the real number x. How many natural numbers n satisfy the equation $$\left[\sqrt{n}\right]=17?$$ A. 17
B. 34
C. 35
D. 36
E. 38

We see that the smallest value n can be is 17^2 = 289 since √289 = 17 and [√289] = [17] = 17.

The largest value n can be is 1 less than 18^2, i.e., n = 18^2 - 1 = 323.

We see that since √323 is still between 17 and 18, we have [√323] = 17 (but √324 = 18 and [√324] = [18] = 18).

Thus the number of natural numbers n can be is all the natural numbers between 289 and 323, inclusive.

There are 323 - 289 + 1 = 35 natural numbers between 289 and 323, inclusive.

Answer: C