Question

Arătați ca ultima cifra a produsului ×(×+1) poate fi doar 0,2sau 6 pentru orice numar natural ×

Answer 1

daca Uc(x) = 0   ⇒   Uc(x+1)=1        Uc[x(x+1)] = 0

" " " " " " " " =1           " " " "  "   2         " " " " "  " "    2

 " " " " " " "    2           " " " " " " " 3       " " " " " " " "  "6

" " " "  " " " " "3           " " " " " " ""4       " " " " " "  "" 2

" " " " " "  ""  " 4         " " " " " "  ""5      " " " " " " " " ""0

" " " " " " " "  5           ' ' '"" " " " "  6      " " "" "   ""  ' 0

                   6                            7                         2

                  7                               8                       6

                  8                              9                         2

                 9                                0                           0