Question 66
a) Verify that if $a \in \{1,2,4\}$, then $n(a+n)$ is not a perfect square for any positive integer $n$.
b) Verify that if $a=2^{k}$ with $k \geq 3$, then there exists a positive integer $n$ such that $n(a+n)$ is a perfect square.
c) Verify that if $a \notin \{1,2,4\}$, then there always exists a positive integer $n$ such that $n(a+n)$ is a perfect square.
b) Verify that if $a=2^{k}$ with $k \geq 3$, then there exists a positive integer $n$ such that $n(a+n)$ is a perfect square.
c) Verify that if $a \notin \{1,2,4\}$, then there always exists a positive integer $n$ such that $n(a+n)$ is a perfect square.