[tex]\bf U(89^{37} +88^{38} +81^{39})=[/tex]
[tex]\bf U(9^{37} +8^{38} +1^{39})=[/tex]
[tex]\bf U(9^{37} +8^{38} +1)=[/tex]
[tex]\bf U(9 +8+1)=[/tex] [tex]\boxed{\bf 8}[/tex]
37:2 = 18, rest 1
[tex]\bf U(9^{1}) = 9[/tex]
[tex]\bf U(9^{2}) = 1[/tex] se repeta din 2 in 2 ⇒ [tex]\bf U(9^{37})=U(9^{1}) = 9[/tex]
[tex]\bf U(9^{3}) = 9[/tex]
38:4 = 9, rest 2
[tex]\bf U(8^{1}) = 8[/tex]
[tex]\bf U(8^{2}) = 4[/tex]
[tex]\bf U(8^{3}) = 2[/tex]
[tex]\bf U(8^{4}) = 6[/tex] se repeta din 4 in 4 ⇒ [tex]\bf U(8^{38})=U(8^{2}) = 4[/tex]
[tex]\bf U(8^{6}) = 8[/tex]
Raspuns: [tex]\bf U(89^{37} +88^{38} +81^{39})=[/tex] [tex]\boxed{\bf 8}[/tex]
