Question

Prove that if n is a perfect square, then n+1 can never be a perfect square

Answer 1

Answer:

Proved

Step-by-step explanation:

To prove that if n is a perfect square, then n+1 can never be a perfect square

Let n be a perfect square

$n=x^2$

Let $n+1 = y^2$

Subtract to get

$1 = y^2-x^2 =(y+x)(y-x)$

Solution is y+x=y-x=1

This gives x=0

So only 0 and 1 are consecutive integers which are perfect squares

No other integer satisfies y+x=y-x=1