Question

Determinati ultima cifra a numarului a = 1+$2^{2}$+$3^{3}$+...+$2013^{2013}$

Answer 1

a=1+2²+3³ +......+2013²⁰¹³

a=(1+2013²⁰¹³) *2013/2

2013¹=(.....3)
2013²=(.....9)
2013³=(.....7)
2013⁴=(.....1)
2013⁵=(.....3)

se repeta din 4 in 4         2013:4=503 rest 1  =>2013²⁰¹³=(.......3)

a=[1+(.....3)]*2013/2

a=(.....4) *2013/2

a=(.....2)* 2013

a=(.....6)