Find the remainder when [5^2000] + [13^2000] is divided by 18. Pls show the working also.

the remainder will be 0 since aⁿ + bⁿ is always divisible by a + b.

({5^2000}+[13^2000])%18=??????????????????????

13/18=remiander=13or-5

{[5^2000] +  (-5^2000)}%18

2*25^1000

25%18=7                  note:r is for remiander

r(2*7^1000)=r(2*49^500)=(2*(-5)^500)=it goes ontill   (7^7)*-350=7*350*(-5)^3=-125*350*7=-1*8*7=-2=+16

so remainder  is 16.

please approve.

the answer is 0 since aⁿ + bⁿ is always divisible by a+b