Question

Which of the following digits is ruled out in the units place of ${12}^n+1$ for every positive integer $n$?

• A. $1$
• B. $2$
• C. $5$
• D. $7$

Answer 1

Answer: (A), (B)

The correct options are
A $1$
B $2$

${12}^n+1$
$2$ has cyclicity $=4$
so checking $n=1,{12}^1+1\equiv 2^1+1\equiv 3$
$n=2,{12}^2+1\equiv 2^2+1\equiv 5$
$n=3,{12}^3+1\equiv 2^3+1\equiv 9$
$n=4,{12}^4+1\equiv 2^4+1\equiv 7$
so $\left(1\right)$ is not coming.