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Topic: Divisibility question
Replies: 5   Last Post: Sep 13, 2013 1:26 PM

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 S.K.R. de Jong Posts: 2 Registered: 8/28/13
Divisibility question
Posted: Aug 28, 2013 8:24 PM

Let N be a nonzero positive integer. We would like to find the
smallest positive integer P(N) such that all integers less than, or equal
to, N divide P(N) evenly. The question is, is there a value of N beyond
which there exists no P(N) satisfying the requirement above?

One can readily (i.e. by means of a quickly put together brute-
force little program) find P(N) for all N < 29 (P(28) being
80,313,433,200) but after a few computer hours there is still no P(29).

I just wonder if it is a matter of more computing power or
whether there are good number theoretic reasons to think (or to prove)
that there is no P(N) for a sufficiently large N.

Date Subject Author
8/28/13 S.K.R. de Jong
8/28/13 Virgil
8/28/13 quasi
8/30/13 Brian Q. Hutchings
9/11/13 Brian Q. Hutchings
9/13/13 Brian Q. Hutchings