Question 18148
<p>Yes, lots of them. This is shown below</p>

<p>There is a theorem, called the fundamental theorem of arithmatic. Amongst other things it says that any whole number can be written as the product of primes. If we chose a number x, we can write it as this product of primes.</p>

{{{x=p[1]*p[2]*p[3]*...}}}

<p>Now consider {{{3x}}} and much more interestingly {{{(3x)^2}}}.</p>

{{{3x=3*p[1]*p[2]*p[3]*...}}}

{{{(3x)^2=3*3*p[1]*p[1]*p[2]*p[2]*p[3]*p[3]*...}}}
{{{(3x)^2=9*p[1]*p[1]*p[2]*p[2]*p[3]*p[3]*...}}}

<p>As you can see {{{(3x)^2}}} is a square number divisible by 9. I've just realised we didn't actually need the stuff about the primes, but it's good to learn something new everyday :D</p>

<p>For your enjoyment, here are three really big square numbers divisible by 9 that I worked out</p>

<ul>
<li>290865928967208697537677954155146591215027084823761634916418981868464451672735642563258575025</li>
<li>377757024764443692555739771423286715885160196068990002369</li>
<li>287239467617910266150742450417499640849213343093880946478917496351351184155930613119360893088100381830756</li>
</ul>

<p>Hope that helps</p>

<p>Kev</p>