Sicherman Dice (proof using factoring)
What combination of sliders still gives 6-sided dice?
See these links for more information:
https://en.wikipedia.org/wiki/Sicherman_dice
http://buzzard.ups.edu/courses/2010spring/projects/jenkins-sicherman-dice-ups-434-2010.pdf
https://www.math.upenn.edu/~wilf/gfologyLinked2.pdf
https://outofthenormmaths.wordpress.com/2012/03/22/dice-and-dissection-a-puzzle/#more-956
https://web.math.ucsb.edu/~padraic/mathcamp_2010/class_generating_functions/lecture3_dice.pdf