Question

Aflati pentru care $\frac{4n+7}{n-1}$ este numar natural.

Answer 1

$\frac{4n+7}{n-1}$∈N => n-1 | 4n+7.
n-1 | n-1 => n-1 | 4(n-1) <=> n-1 | 4n-4.

n-1 | 4n+7
n-1 | 4n-4
---------------
n-1 | (4n+7)-(4n-4) <=> n-1 | 11 => (n-1)∈$D_{11}=${1;11}.
n-1=1=>n=2
n-1=11=>n=12.

Solutie n∈{2;12}.