Question

Determinați ultima cifra.


${89}^{37} + {88}^{38} + {81}^{39}$

${68}^{86}$
Dau coroana!! ​

Answer 1

$\bf U(89^{37} +88^{38} +81^{39})=$

$\bf U(9^{37} +8^{38} +1^{39})=$

$\bf U(9^{37} +8^{38} +1)=$

$\bf U(9 +8+1)=$  $\boxed{\bf 8}$

37:2 = 18, rest 1

$\bf U(9^{1}) = 9$

$\bf U(9^{2}) = 1$       se repeta din 2 in 2 ⇒ $\bf U(9^{37})=U(9^{1}) = 9$

$\bf U(9^{3}) = 9$

38:4 = 9, rest 2

$\bf U(8^{1}) = 8$

$\bf U(8^{2}) = 4$

$\bf U(8^{3}) = 2$

$\bf U(8^{4}) = 6$       se repeta din 4 in 4 ⇒ $\bf U(8^{38})=U(8^{2}) = 4$

$\bf U(8^{6}) = 8$

Raspuns: $\bf U(89^{37} +88^{38} +81^{39})=$ $\boxed{\bf 8}$