Recently, I found this problem online:
Given $a+b=1$ and $a^2+b^2=2$, find $a^7+b^7$.
Although I could've solved it by substituting the first equation into the second and then using the quadratic formula; the way the question was set up, I suspected that there was a shortcut. However, I couldn't find the solution to the problem on that website, so I'm asking here:
If you are given $a+b$ and $a^2+b^2$, is there a shortcut to finding $a^n+b^n$?