Thursday, February 24, 2011

Pronic number

A pronic number is a number which is the product of two consecutive integers,
that is, n*(n + 1).


For every integer a, prove that

(a^2 + a - 1)(a^2 + 3a + 1) + 1

is a product of two consecutive integers.
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1 comment:

  1. PaulApril 15, 2011 at 2:09 AM

    We need to show that (a^2 + a - 1)(a^2 + 3a + 1) + 1 Is the product of two terms that differ by 1. so a little re-arranging gives us:-

    (a^2 + 2a - 1)(a^2 + 2a) which equals:-
    (a^2 + a - 1)(a^2 + 3a + 1) + 1

    Paul.

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