Question

Calculati ultima cifra a numarului A=23^23+24^24+25^25+27^27+28^28+29^29!!!Va rog ajutatima!!!!!!

Answer 1

A=23^23+24^24+25^25+27^27+28^28+29^29
23^23=23^4*5+3 (rest)=>23^3=....7 ultima cifra
24^24=6 (orice nr. terminat in 4 ridicat la o putere para =6) ultima cifra
25^25=5 ( orice nr. terminat in 5 ridicat la orice putere =5)
27^27=27^4*6+3 (rest)=27^3=3 ultima cifra
28^28=28^4*7+0 =>28^0=1 ultima cifra
29^29=9 ultima cifra (orice nr terminat in 9 ridicat la orice putere impara =9)
A=7+6+5+3+1+9=31=1ultima cifra
Orice nr. care se terimina in 2,3,7 si 8 ridicate la orice putere nenula se repeta din 4 in 4 ( de asta am impartit la 4) .

Answer 2

A=23²³+24²⁴+25²⁵+27²⁷+28²⁸+29²⁹

1. u(23²³) = ?              2. u(24²⁴)= ?                   3. u(27²⁷)=?

 

23:4= 5(r.3)                  24:2= 12(r.0)                27:4= 6(r.3)

 

u(23³)= 7                       u(24⁰)= 1                      u(27³)= 3

 

 

4. u(28²⁸)=?                     5. u(29²⁹) = ?

 

28:4= 7(r.0)                     29: 2= 14(r.1)

 

u(28⁰)=1                          u(29¹) = 9

 

 

A = 7+ 1+ 3+ 1+ 9

 

    = 10 +10+ 1

 

    = 21

u(A) = 1