Mathematics Stack Exchange is a question and answer site for people studying math at any level and professionals in related fields. Join them; it only takes a minute:

Sign up
Here's how it works:
  1. Anybody can ask a question
  2. Anybody can answer
  3. The best answers are voted up and rise to the top

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

share|cite|improve this question
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

I see no need to retype the answer given here, which is the first result when putting the title of this question into Google.

share|cite|improve this answer
Much more is known --- the product of two or more consecutive positive integers is never a power (meaning, a square or higher power). The paper by Erdos and Selfridge is freely available at – Gerry Myerson Feb 15 '13 at 2:14

Your Answer


By posting your answer, you agree to the privacy policy and terms of service.

Not the answer you're looking for? Browse other questions tagged or ask your own question.