Question

The product of four consecutive natural numbers is 840. Find the numbers.
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Answer 1

Answer:

If n

is the smallest of the four consecutive positive integers, then

840=n(n+3)⋅(n+1)(n+2)

=((n2+3n+1)−1)((n2+3n+1)+1)

=(n2+3n+1)2−1

.

Hence, n2+3n+1=29

so that n=4.

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