Va rog , ajutati - ma !!!

Aflati cu rezolvare ultima cifra a nr. :

1. 68 la puterea 86

2. 71 la puterea 10000001

3. 1009 la puterea 9001

4. 77 la puterea 36 + 77 la puterea 37 + 77 la puterea 38 + 77 la puterea 39

5. 89 la puterea 37 + 88 la puterea 38 + 87 la puterea 39

Va Multumesc Extrem De Mult Ca Ma - ti Ajutat !!!

1

Răspunsuri

Cel mai inteligent răspuns!
2014-08-20T14:12:33+03:00
1)  68^{86} =U(8^86)=u(8^21^*4+8^2)=u(8^4)*u(8^2)=6*4=24=u(4) =4
2)
 71^{10000001} =u(110000001)=u(1)=1
3)
  1009^{9001} =u(9^9001)=u(9^2250^*4+9^1)=u(9^4)*u(9^1)=1*9=u(9)=9
4)
 77^{36} =u(7^36)=u(7^9^*4)=u(7^4)=u(1) =1
     77^{37} =u(7^37)=u(7^9^*4+7^1)=u(7^4)*(7^1)=1*7=u(7) =7
     77^{38} =u(7^38)=u(7^9^*4+7^2)=u(7^4)*u(7^2)=1*9=u(9) =9
     77^{39} =u(7^39)=u(7^9^*4+7^3)=u(7^4)*u(7^3)=1*3=u(3)=3
le adun 1+7+9+3=20 ,deci ultima cifra =0
5)  89^{37} =u(9^37)=u(9^4+9^1)=u(9^4)*u(9^2)=1*9=u(9) =9
     88^{38} =u(8^38)=u(8^9^*4+9^1)=u(9^4)*u(8^2)=6*4=24=u(4)=4
     87^{39} =u(7^39)=u(7^9^*4+7^3)=u(7^4)*u(7^3)=1*3=u(3)=3
le adun 9+4+3=16 , adica ultima cifra e 6
4 4 4