isi-entrance 2015 Q3

isi-entrance · India · UGA 4 marks Number Theory Quadratic Diophantine Equations and Perfect Squares
If $n$ is a positive integer such that $8 n + 1$ is a perfect square, then
(a) $n$ must be odd
(b) $n$ cannot be a perfect square
(c) $2 n$ cannot be a perfect square
(d) none of the above.
(c) If $8 n + 1 = m ^ { 2 }$, then $2 n$ is a product of two consecutive integers.
If $n$ is a positive integer such that $8 n + 1$ is a perfect square, then\\
(a) $n$ must be odd\\
(b) $n$ cannot be a perfect square\\
(c) $2 n$ cannot be a perfect square\\
(d) none of the above.