Question

Aratati ca urmatoarele numere naturale se divid cu 2: a) 17la puterea10-7la puterea 10; b) 105la puterea 19+33la puterea17+101la puterea23+57la puterea52; c) 1+11+111+........+11....1 2012 cifre.

Answer 1

a) 17¹⁰-7¹⁰
Uc(17¹⁰-7¹⁰)=Uc(7¹⁰-7¹⁰)=0  deci divizibil cu 2


b) 105¹⁹+33¹⁷+101²³+57⁵²
Uc(105¹⁹+33¹⁷+101²³+57⁵²)=
=Uc(5+3¹⁷+1²³+7⁵²)=
=Uc(5+3¹+1+7⁴)=
=Uc(5+3+1+1)=
=Uc(10)=0   deci divizibil cu 2


c) 1+11+111+........+11....1 2012 cifre
Uc(1+11+111+........+11....1 2012 cifre)=
=Uc(1+1+1+....1 nr termeni 2012)=
=Uc(1×2012)=2 deci divizibil cu2