Weekly Challenge 34: Googol
A googol is the number
$10^{100}$. What is the smallest whole number $n$ for which
$$
n^4-6n^2> \mbox{googol}?
$$
Can you carefully write out the number on the left-hand side of
this inequality for this value of $n$ in base 10?
Did you
know ... ?
Although computers are very useful in checking calculations in
number theory, it is very difficult to use them to perform
calculations involving very, very large numbers. A googol is a big
number, but a googolplex, defined to be $10^{\mbox{googol}}$ is
unimaginably larger. Such gigantic numbers do make appearances in
mathematics from time to time and require the power of pure thought
and mathematics to yield to analysis. Rather amusingly, the Googol
Corporation call their headquarters 'the googolplex'.