mersenneforum.org - View Single Post - Williams' sequence 4*5^n-1 (A046865)

geoff · 2006-07-28, 03:34

For the sequence 4*5^n-1, can anyone explain why all the factors end in 1 or 9 when n is odd?

I haven't tested many examples, but I think all the odd factors of k*5^n-1 end in 1 or 9 when n is odd and k is a square. Can anyone explain this?

2006-07-28, 03:34	#28
geoff Mar 2003 New Zealand 13×89 Posts	*Factors of 45^n-1** For the sequence 45^n-1, can anyone explain why all the factors end in 1 or 9 when n is odd? I haven't tested many examples, but I think all the odd factors of k5^n-1 end in 1 or 9 when n is odd and k is a square. Can anyone explain this?