Question

If n is a positive integer such that 8n + 1 is a perfect square then can 2n be a perfect square

Answer 1

yes 2n can be a perfect square

Answer 2

Answer: No

Step-by-step explanation:

8n+1=x^2

8n+4=x^2+3

2n+1=(x^2+3)/4

2n=[(x^2+3)/4]-1

2n=(x^2-1)/4

Subtracting 1 from a perfect square integer do not give a perfect square.

Thus 2n is not a perfect square for the given condition.