# Task 1. (10 points)

How many natural numbers $n$ exist such that the equation $n x-12=3 n$ has an integer solution

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# Solution.

Since $n x-12=3 n \Rightarrow x=3+\frac{12}{n}$, the condition of the problem is satisfied if 12 is divisible by $n$. Therefore, $n$ can take the values $1,2,3,4,6,12$.

Answer. 6

| Criterion | Evaluation | Points |
| :---: | :---: | :---: |
| Complete solution. | + | 10 |
| All main logical steps of the solution are provided.  Integer values of $\boldsymbol{n}$ are calculated. |  |  |
| All main logical steps of the solution are provided.  The answer is incorrect. | $+/ 2$ | 5 |
| The answer is correct.  The solution is missing or incorrect. | $\mp$ | 2 |
| The solution does not meet any of the criteria described above. | $-/ 0$ | 0 |
| Maximum score | 10 |  |