We know that an
exists that equal to
This
is very powerful in competition math problems. Usually coming up on JMO and AMO geo problems. The Euler Line intersects the radical axis at
where
is the number of composite factors the radius has. This theorem is also used in Newton's Sums, as the
th root unity is the same thing as
Finally, you'll se it in combo! The number ways you can shuffle
things into
items where
is the number of partitions in an item is the
My coaches Iyer Sir and Barnes approved this nice lemma.