# Product of $5$ consecutive integers cannot be perfect square

How can we prove that the product of $5$ consecutive integers cannot be a perfect square?

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No.${}{}{}{}{}$ –  Will Jagy Feb 14 '13 at 23:54
Did you mean 5 consecutive natural numbers? Otherwise there's $0$, $1$, $2$, $3$, $4$ and product $0=0^2$. –  zaarcis Feb 15 '13 at 0:01
@WillJagy: what does this 'No' refer to? –  Berci Feb 15 '13 at 0:06
What if $a=0$ ? –  zaarcis Feb 15 '13 at 0:09
@Berci the original version of the question simply said 'prove', not 'how can we prove?'. –  Steven Stadnicki Feb 15 '13 at 0:11