Question

determinati numerele naturale x ptr fractia 2x+3/15 este sububitara si ireductibila.

Answer 1

2x+3/15 subunitara ⇔2x+3<15⇔2x<12⇔x<6, x∈ N⇒x∈{0;1;2;3;4;5}
dar 2x+3/15 ireductibila⇔(2x+3,15)=1
daca x=0⇒2x+3=2·0+3=3,dar (3,15)=3⇒nu convine
daca x=1⇒2x+3=2·1+3=5,dar (5,15)=5⇒nu convine
daca x=2⇒2x+3=2·2+3=4+3=7,dar (7,15)=1⇒convine!
daca x=3⇒2x+3=2·3+3=9,dar (9,15)=3⇒nu convine
daca x=4⇒2x+3=2·4+3=11,dar (11,15)=1⇒convine!
daca x=5⇒2x+3=2·5+3=13,dar(13,15)=1⇒convine!
Deci, x∈{2;4;5}.