Question

take two consecutive odd numbers find the sum of their squares and then add 6 to the result then prove that new number is always divisible by 8

Answer 1

I have taken 2n+1 and 2n-1 as odd numbers

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Answer 2

Let the two consecutive odd numbers be 1 and 3.

Sum of their squares = 1^2 + 3^2

                                    = 1 + 9

                                    = 10.


Now, Add 6 to the result = 10 + 6

                                          = 16.


Now, the resultant number should be divisible by 8 = 16/8

                                                                                        = 2.


Therefore the new number is always divisible is divisible by 8.


Hope this helps!