2bornot2b
  • 2bornot2b
Prove that the product of 4 consecutive integers is 1 less than a perfect square.
Mathematics
chestercat
  • chestercat
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anonymous
  • anonymous
what have you tried?
anonymous
  • anonymous
oops type-0! :( \[n(n+1)(n+2)(n+3)\]
2bornot2b
  • 2bornot2b
Tried many things in vain

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anonymous
  • anonymous
Kidds stuffs, Let the consecutive integers be \( (n - 1), n, (n + 1), (n + 2) \) Expanding: \[n^4 + 2n^3 - n^2 - 2n= (n^2 + n - 1)^2-1 \]
anonymous
  • anonymous
Nice work ffm!

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