Question

Algebraically prove that the difference of the squares of any two consecutive integers is an odd integer.

Answer 1

Can you prove it using an example?

Answer 2

yeh

Answer 3

let x and x+1 be consecutive integers.Clearly x is an integer.
\[(x+1)^2-x^2=x^2+2x+1-x^2=2x+1\]
Because x is an integer
therefore 2x+1 is an odd integer.

Answer 4

Thank you good and brief explanation, @sshayer !