12

Part of 2015 ASDAN Math Tournament

Problems(2)

Source:

The rectangular faces of rectangular prism

A

have perimeters

12

16

24

. The rectangular faces of rectangular prism

B

have perimeters

12

16

20

V_A

denote the volume of

A

V_B

denote the volume of

B

V_A-V_B

Source:

Find the smallest positive integer solution to the equation

2^{2^k}\equiv k\pmod{29}