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N={0,1,2,3,...........,n,...............+∞]
Pt n=0: 10^0 + 2 / 3 =1+2 / 3 = 1∈N
Pt n=1: 10^1 +2 / 3 = 12/3 = 4∈N
..........................................................
Presupunem adevarat pt n=k, adica
f(k) = 10^k +2 / 3 ∈ N
V.d. pt n=k+1
f(k+1) = 10^(k+1) + 2 / 3 = 10*10^k + 2 / 3 = 10(10^k +2) -18 / 3 =
10(10^k + 2) / 3 - 18/3 =
10*f(k) - 6 = 10*M3 -M3, deci multiplu de 3. c.c.t.d.(ceea ce trebuia demonstrat).