Question

2^16 -1 divisible by......17
full process shortcut

Answer 1

(2^16-1)
-------------- =((2^4 x 2^4 x 2^4 x 2^4)-1)/17
17
((16 x 16 x 16 x 16) -1)
= ------------------------- = ((256 x 256) -1)/17
17
(HERE EASY MULTIPLICATION OF THREE DIGIT IS
256 X 256

256
256
------
36(UNIT DIGIT SQUARE)
5 (MIDDLE DIGIT'S PRODUCT'S UNIT DIGIT)
650(25 x 26)
=65536)
65536-1
= -------------=65535/17=3855
17

Answer 2

${x}^{n} - {a}^{n}$
is always divisible by x-a and x+a if n is even. So this will be divisible by both 17 and 15.