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2bornot2b

  • 3 years ago

Prove that the product of 4 consecutive integers is 1 less than a perfect square.

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  1. FoolForMath
    • 3 years ago
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    what have you tried?

  2. ZombiePig
    • 3 years ago
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    oops type-0! :( \[n(n+1)(n+2)(n+3)\]

  3. 2bornot2b
    • 3 years ago
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    Tried many things in vain

  4. FoolForMath
    • 3 years ago
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    Kidds stuffs, Let the consecutive integers be \( (n - 1), n, (n + 1), (n + 2) \) Expanding: \[n^4 + 2n^3 - n^2 - 2n= (n^2 + n - 1)^2-1 \]

  5. ZombiePig
    • 3 years ago
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    Nice work ffm!

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