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Determinați ultima cifra.


[tex] {89}^{37} + {88}^{38} + {81}^{39} [/tex]

[tex] {68}^{86} [/tex]
Dau coroana!! ​


Determinați Ultima Cifra Tex 8937 8838 8139 Textex 6886 TexDau Coroana class=

Răspuns :

[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]