Question

Ultima cifra a numarului 2 la puterea 42 + 3 la puterea 42

Answer 1

Uc(2⁴²+3⁴²)=Uc(2⁴²)+Uc(3⁴²)=4+9=13=3
2¹=2                                  3¹=3
2²=4                                  3²=9
2³=8                                  3³=27
2⁴=16                                3⁴=81
2⁵=32                                3⁵=243
42:4=10 rest 2

Answer 2

   
[tex]U(2^{42} + 3^{42}) = \\ =U(2^{42}) + U(3^{42}) = \\ =U(2^{4\times 10+2}) + U(3^{4\times 10+2}) = \\ =U\Big[\Big(2^{4}\Big)^{10}\times 2^2}\Big] +U\Big[\Big(3^{4}\Big)^{10}\times 3^2}\Big] = \\ =U\Big[16^{10}\times 2^2}\Big] +U\Big[81^{10}\times 3^2}\Big] = \\ =U\Big[6\times 4}\Big] +U\Big[1\times 9}\Big] = \\ U( 24 + 9) = U(33) = \boxed{3} [/tex]