Question

Example 1 : Prove that the square of an odd integer decreased by 1 is a multiple of 8.​

Answer 1

Step-by-step explanation:

HOPE IT WILL HELP YOU. .. ..

Answer 2

Answer:

Step-by-step explanation:

Let P(n)= $n^{2}$ - 1

∴ P(1) = $1^{2}$  - 1 = 1 - 1

         = 0

Proof : By the division theorem any number can be expressed in one of the forms 4q,4q+1,4q+2,4q+3

Squaring each of these gives :

(4q+1)2=16q2+8q+1=8(2q2+q)+1

(4q+3)2=16q2+24q+9=8(2q2+3q+1)+1

My answer :

I think this proof is invalid as it does not prove ' the square of any odd number is 1 more than a multiple of 8. ' is true for any odd number as it does not prove for the odd number (2n+1) or (2n−1).