Răspuns :
[tex]u(2^1)=2[/tex]
[tex]u(2^2)=4[/tex]
[tex]u(2^3)=8[/tex]
[tex]u(2^4)=6[/tex]
[tex]u(2^5)=2[/tex]
Observam ca o ultima cifra a puterilor de 2 se repeta din 4 in 4 puteri
83:4=20 rest 3
Daca da rest 3 la impartirea la 4, atunci
[tex]u(2^{83})=u(2^3)=8[/tex]
La fel se repeta si la puterile de 3, din 4 in 4
84:4=21 rest 0
Daca da rest 0, se considera rest 4
[tex]u(3^{84})=u(3^4)=u(81)=1[/tex]
[tex]u(2^{83}+3^{84})=8+1=9[/tex]
[tex]u(2^2)=4[/tex]
[tex]u(2^3)=8[/tex]
[tex]u(2^4)=6[/tex]
[tex]u(2^5)=2[/tex]
Observam ca o ultima cifra a puterilor de 2 se repeta din 4 in 4 puteri
83:4=20 rest 3
Daca da rest 3 la impartirea la 4, atunci
[tex]u(2^{83})=u(2^3)=8[/tex]
La fel se repeta si la puterile de 3, din 4 in 4
84:4=21 rest 0
Daca da rest 0, se considera rest 4
[tex]u(3^{84})=u(3^4)=u(81)=1[/tex]
[tex]u(2^{83}+3^{84})=8+1=9[/tex]
2¹=..2
2²=..4
2³=..8
2⁴=..6
2⁵=..2 => 83:4=20rest3<=>u.c.2⁸³=8
3¹=..3
3²=..9
3³=..7
3⁴=..1
3⁵=..3 => 84:4=21rest0<=>u.c.3⁸⁴=1
------------------------------------------------------
u.c. 2⁸³ + 3⁸⁴ = 8 + 1 = 9
2²=..4
2³=..8
2⁴=..6
2⁵=..2 => 83:4=20rest3<=>u.c.2⁸³=8
3¹=..3
3²=..9
3³=..7
3⁴=..1
3⁵=..3 => 84:4=21rest0<=>u.c.3⁸⁴=1
------------------------------------------------------
u.c. 2⁸³ + 3⁸⁴ = 8 + 1 = 9