Show that the square of any odd integer is odd

[winsome]

show that the square of any odd integer is odd, use this fact to justify the statement "if p2
is even , then p is also even

 

[micromass]

Well, what did you try already? If we know where you're stuck, then we'll know where to help...

 

[gauss^2]

A good first step is noticing that

...
-5 = 2*(-3) + 1
-3 = 2*(-2) + 1
-1 = 2*(-1) + 1
1 = 2*0 + 1
3 = 2*1 + 1
5 = 2*2 + 1
...

 

[Amergin]

(2x+1) is odd. (2x+1)^2=4x^2+4x+1 but 4x^2+4x is even and even +1 gives odd.
So (2x+1)^2 is odd