isi-entrance 2021 Q17

isi-entrance · India · UGA Number Theory GCD, LCM, and Coprimality
Define $a = p ^ { 3 } + p ^ { 2 } + p + 11$ and $b = p ^ { 2 } + 1$, where $p$ is any prime number. Let $d = \operatorname { gcd } ( a , b )$. Then the set of possible values of $d$ is
(A) $\{ 1,2,5 \}$.
(B) $\{ 2,5,10 \}$.
(C) $\{ 1,5,10 \}$.
(D) $\{ 1,2,10 \}$.
Define $a = p ^ { 3 } + p ^ { 2 } + p + 11$ and $b = p ^ { 2 } + 1$, where $p$ is any prime number. Let $d = \operatorname { gcd } ( a , b )$. Then the set of possible values of $d$ is\\
(A) $\{ 1,2,5 \}$.\\
(B) $\{ 2,5,10 \}$.\\
(C) $\{ 1,5,10 \}$.\\
(D) $\{ 1,2,10 \}$.