View source for 2007 SMT Algebra Round Problem 6

==Problem==
What is the largest prime factor of <math>4^9+9^4</math>?

==Solution==
By just bashing it out, we get <math>4^9=2^{18}=2^{10}\times2^8=1024\times256=262144</math> and <math>9^4=9^2\times9^2=81\times81=6561</math>. After adding these two up, we get <math>4^9+9^4=262144+6561=268705</math>. By just looking at this, we see that it is divisible by <math>5</math>, so let's divide by <math>5</math> to get <math>53741</math>. After trying all the primes from <math>7</math> to <math>61</math> (<math>5</math> won't work because this number does not end in <math>5</math> or <math>0</math>), we get that this number is divisible by <math>61</math>, and our quotient is <math>881</math>. Because no prime less than <math>61</math> divided <math>53741</math>, they won't divide <math>881</math> either, and because <math>61^2 > 881</math>, <math>881</math> must be prime, so our primes are <math>5, 61,</math> and <math>881</math>. Because <math>881</math> is the greatest out of all of these, our answer is <math>\boxed{\mathrm{881}}</math>.

~Yuhao2012