Can someone help me understand how to do this GRE Quant Question?

[shicode]

What is the remainder when 13^17 + 17^13 is divided by 10?

PS: This is the 26th question in Chapter 13 of the 5lb Manhattan Prep Book (Pg 498)

[TakeruK]

Hint 1: The remainder when dividing by 10 is always the ones digit (i.e the last digit) of a number.

Hint 2: When you have crazy large numbers like this, you are rarely expected to actually calculate the entire number. Instead, look for a pattern in the part of the number you care about and then use that pattern to get your answer.

[JohnKim]

Wow this is interesting. So TakeruK, there is no proper answer? I am still confused with your answer, I am very sorry.

Newbie here, and I would like to be notified of the replies

 

[chayan13]

13^17 will have 3 as the last digit and 17^13 will have 7 as the last digit and when they both are added will give you 0 at the units place. that's done now to get the remainder when divided by 10 you get unit digit as remainder, here 0 is the remainder the answer is 0. I hope i am right.