Have you actually used fermat's Little theorem?
It states that for any prime number we have mod
Here we divide by , thus we have mod 17 for any number .
Use this fact and observe that mod 17
(*) here we used fermat's theorem.
Now you try mod 17
ok i've checked my answer an i think i made a stupid mistake at the end,
36= 2 mod 17 and 31 = -3 mod 17 therefore
36^(50) + 30^(19) = ( 2^50 + ((-3)^19 ) mod 17
= (1 + -27) mod 17 using fermat's little theorem
= 8 mod 17
therefore the remainder is 8 (i had 9 here instead making a stupid mistake) is this correct then,
really sorry i dont know how to use latex yet but i have my exams soon so im busy revising, thanks for any help