Determine, with proof, the greatest common divisor of this sequence of positive integers :
{16^M + 10M – 1; M = 1, 2, .......}

It suffices to work on small values of m.

2^(4m)-1 mod25 gives the cycle{15,5,20,10,0}

10m mod25 gives the cycle {10,20,5,15,0}.

Adding these gives 0 mod25 in all cases.

Let m = 1. Since 16+10-1 =25, there can be no larger common divisor of the sequence.

Posted by broll on 2016-01-19 08:39:20