1x2x3x4 + 1 = 25 = 5^2

3x4x5x6 + 1 = 361 = 19^2

...

Prove that the product of 4 whole consecutive numbers plus one is always a perfect square.

bye

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- Apr 11th 2005, 11:36 AMtheprofAlways square

1x2x3x4 + 1 = 25 = 5^2

3x4x5x6 + 1 = 361 = 19^2

...

Prove that the product of 4 whole consecutive numbers plus one is always a perfect square.

bye - Apr 11th 2005, 12:54 PMpaultwang
If by whole numbers you mean

**Z+**,

For any whole number n,

n*(n+1)*(n+2)*(n+3)+1

= n^4+6*n^3+11*n^2+6*n+1

= (n^2+3*n+1)^2

(n^2+3*n+1)^2 is the square of (n^2+3*n+1), and (n^2+3*n+1) is an integer. - Apr 12th 2005, 07:17 AMtheprofQuote:

Originally Posted by**paultwang**