[tex] \frac{25}{4n+1} [/tex] ∈ Z => 4n+1 | 25 => (4n+1)∈[tex] D_{25} [/tex]={-25, -5, -1, 1, 5, 25}.
4n+1=-25 => 4n=-26 => n=[tex] -\frac{26}{4} [/tex] ∉ Z
4n+1=-5 => 4n=-6 => n=[tex]- \frac{6}{4} [/tex] ∉ Z
4n+1=-1 => 4n=-2 => n=[tex] -\frac{2}{4} [/tex] ∉ Z
4n+1=1 => 4n=0 => n=0 (solutie)
4n+1=5 =>4n=4 => n=1 (solutie)
4n+1=25 => 4n=24 => n=6 (solutie)
Deci n∈{0,1,6}.
