if m is equal to n square - n is an integer, then m square - 2m is divisible by what number

Dear student,

Given,
m=n^2-n => m=n(n-1)______(1)

Now, m^2-2m = m(m-2) = n(n-1)[n(n-1)-2]

=n(n-1)[n^2-n-2]

=n(n-1)(n+1)(n-2)

=(n-2)(n-1)(n)(n+1)

Which is a product of 4 consecutive numbers so, it's divisible by 4*3*2*1 i.e. 24.

Regards

  • 4
Dear student,

Given,
m=n^2-n => m=n(n-1)______(1)

Now, m^2-2m = m(m-2) = n(n-1)[n(n-1)-2]

=n(n-1)[n^2-n-2]

=n(n-1)(n+1)(n-2)

=(n-2)(n-1)(n)(n+1)

Which is a product of 4 consecutive numbers so, it's divisible by 4?3?2?1 i.e. 24..

Regards
  • 0
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