Question

Is $1^{11}+2^{11}+3^{11}+4^{11}$ divisible by $5$? Explain

Answer 1

$1^{11}+2^{11}+3^{11}+4^{11}$

last digit of $1^{11}=1$

last digit of $2^{11}=8$

last digit of $3^{11}=7$

last digit of $4^{11}=4$

The last digit we have $20.$

which gives $0$ and which is always divisible by $5.$