Let be square free. Consider .
For which conditions on is ?
with the abc-formula we have that consists of the numbers
To make sure has the desired property we must have for some number .
That is, .
This number can ofcourse be freely chosen.
Then we must choose that satisfy this relation. Thus we must choose a such that
there exists a composite number that satisfies
wich is, the same as saying must be a composite number. Only then we can choose such that .
And we've found such that has the desired property.
no, I Edited my post ;p
with the abc-formula we have that consists of the numbers
To make sure has the desired property we must have for some number .
That is, .
This number can ofcourse be freely chosen.
Then we must choose that satisfy this relation. Thus we must choose a such that
there exists a number that satisfies
wich is, the same as saying . Only Then we can choose such that .
And we've found such that has the desired property.