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Aflati pentru care [tex] \frac{4n+7}{n-1} [/tex] este numar natural.

Răspuns :

[tex] \frac{4n+7}{n-1} [/tex]∈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)∈[tex] D_{11}= [/tex]{1;11}.
n-1=1=>n=2
n-1=11=>n=12.

Solutie n∈{2;12}.