a) Fie A = {n+1000/n+17 | n∈N}. Aratati ca multimea A ∩ N are un singur element.
b)Determinati elementele multimii A = { x∈N| 7x-5/2x+3 ∈ Z }

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(n+1000)/(n+17)= (n+17+983)/(n+17)=1+983(n+17)∈N

n+17∈D983={1;983}

n+17=1,n=-16∉N

n+17=983, n=966∈N

pt n=17=-1 sau -983 n∉N

deci avem o singura solurie naturala, n=966

b) (7x-5)/(2x+3)∈Z, (14x-10)/(2x+3)∈Z, (14x+21-31)/(2x+3)∈Z, 7-31/(2x+3)∈Z

31/(2x+3)∈Z

2x+3∈{{-31;-1;1;31}

2x∈{-34;-4;-2;28}

x∈{-17;-2;-1;14}

{-17;-2;-1;14}∩N={14}

deci singura valoare naturala este 14