The units digit in the product $\left(5^{2}+1\right)\left(5^{3}+1\right)\left(5^{23}+1\right)$ is
(A) 0
(B) 1
(C) 2
(D) 5
(E) 6
The units digit in the product $\left(5^{2}+1\right)\left(5^{3}+1\right)\left(5^{23}+1\right)$ is
(A) 0
(B) 1
(C) 2
(D) 5
(E) 6

## Solution

Since $5^{2}, 5^{3}$ and $5^{23}$ all end in 5 , then $5^{2}+1,5^{3}+1$ and $5^{23}+1$ all end in 6 . When we multiply these three numbers together their product must also end in a 6 .

ANSWER: (E)