Show that (5125 - 1)/(525 - 1) is composite.
Solution
Put x = 525. Then (5125-1)/(525-1) = x4+x3+x2+x+1 = (x2+3x+1)2 - 5x(x+1)2 which has factor (x2+3x+1-513x-513) which is obviously > 1 and < x4+x3+x2+x+1.
© John Scholes
jscholes@kalva.demon.co.uk
25 Nov 2003
Last updated/corrected 25 Nov 2003