Let n be a positive integer. Find a formula for the units digit of (11+sqrt(111))^n.

I have found the formula for the units digit, but I'm still working on the proof.  here is the formula

let M(n)=n-4*[n/4]

let U(n)= desired unit digit

then U(n)=[1/3][15-25M(n)+15*M(n)^2-2*M(n)^3]

or in other words the unit digit cycles thru 1,3,7,5

Posted by Daniel on 2007-05-21 14:47:39