A = (2+1) (2^2+1) (2^4+1) (2^8+1) (2^16+1) (2^32 + 1). Find the units digit in A - 2016

2^1=2

2^2=4

2^4=16

2^8=256

2^16=65536

2^32=1048576

...

If we add 1 to the last digits above, we have the sequence

3,5,{7,7,7,7},{7,7,7,7} ...

But 7*7*7*7=2401, finishes with a 1, so all the groups of 4 7's wont change the last digit.

Hence A ends with a 5 (because 3*5=15 ends with a 5)

and A-2016 ends with a 9 (because 15-6=9)

In fact, A-2016=18446744073709549599 if you bother to know.

Try your deduction skills:

What is the last digit of

B = (2+1) * (2^2+1) * (2^4+1) * (2^8+1) * (2^16+1) * (2^32 + 1) ... * (2^131072+1) * (2^2097152+1) ?

Note: 2097152=2^21