Van Roomen's equation is the degree-45 polynomial equation posed by Adriaan van Roomen as a challenge in 1593. In modern notation it is
 |
where 
is a Chebyshev polynomial of the
first kind and 
is a specified algebraic number. For the main
challenge,
 |
The expanded polynomial begins 
. François Viète
recognized it as the multiple-angle formula
for 
with 
and found all 23 positive roots. The smallest positive solution
of the main challenge is 
.
