Question

Is 46^{999}- 20^{999} divisible by 13 or not. Explain with steps.

Answer 1

46999-20999=26000
As 26 is divisible by 13 then 26000 is also divisible by 13 .
 26000÷13 = 2000
I hope this would help you 

Answer 2

46^999 = (20+26)^999
using binomial expension
(20+26)^999 = 999C0(20)^999 + 999C1{(20)^998}(26) + 999C2{(20)^997}(26)^2 + ------------------- + 999C999(26)^999
(20+26)^999 = 20^999 + 26[999C1(20)^998 + 999C2{(20)^997}(26) + -------------- + 999C999(26)^998]
46^999 = 20^999 + 26(K)              {K = 999C1(20)^998 + -------- + 999C999(26)^998}
46^999 - 20^999 = 26(K)               (26 = is a factor of 13)
hence 46^999 - 20^999 is divisible by 13
i hope you will understand