Suppose that

n

is a positive integer with the properties:\ for any integers

a,b,c

,\

n|abc

implies that

n|ab

or

n|bc

or

n|ac

\

n

is not prime and\

p_(10)|n

, where

p_(i)

is the

i

th prime (i.e.,

p_(1)=2,p_(2)=3,dots

).\ What is the smallest possible value of

n

?

Suppose that n is a positive integer with the properties: - for any integers a,b,c, nabc implies that nab or nbc or nac - n is not prime and - p10n, where pi is the i th prime (i.e., p1=2,p2=3, ). What is the smallest possible value of n