



 
Can the cube of an integer end with one 1? Can it end with 2 ones? three 1's? (Experiment) We can show by induction that there always exists a number ending in k 1's. But there exists (prove this!) B with 0<=B<10 such that 3B ends in A. Show that [B*10^{k1} + N]^{3} ends in k 1's. Hint: binomial expansion. Bonus question: why does this NOT work for squares? What is the next power it does work for? Good Hunting!  


Math Central is supported by the University of Regina and The Pacific Institute for the Mathematical Sciences. 