Question

Prove that:
16^4–2^13–4^5 is divisible by 11

Answer 1

9514 1404 393

Step-by-step explanation:

Each of the numbers can be expressed as a power of 2.

(2^4)^4 -2^13 -(2^2)^5 = 2^16 -2^13 -2^10

Factoring out 2^10 gives ...

= 2^10(2^6 -2^3 -1) = 2^10(64 -8 -1) = 2^10(55)

= (2^10)(5)(11) . . . . a number evenly divisible by 11