Răspuns:
Explicație pas cu pas:
a)
2018^10 = (2018^5)^2 patrat perfect
b)
81^7 = (9^2)^7 = (9^7)^2 patrat perfect
c)
1 + 2 + 3 + ... + 2018 = 2018*2019/2
2*2018*2019/2 = 2018*2019
2018*2019 + 2019 = 2019*(2018 + 1) = 2019*2019 patrat perfect
d)
3^6n+3 + 2*3^6n+2 + 5*3^6n+1 + 4*3^6n
= 3^6n*(3^3 + 2*3^2 + 5*3 + 4)
= 3^6n*(27 + 18 + 15 + 4)
= 64*3^6n
= (8*3^2n)^2 patrat perfect
e)
4^50 + 4^49 + 4^48 = 4^48*(4^2 + 4 + 1) = 21*4^48
21*4^48 : 21 = 4^48
4^48 = (4^24)^2 patrat perfect
4^48 = (4^16)^3 cub perfect
