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Question

What is the remainder when 1317+1713 is divided by 10

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Solution

The remainder when dividing on integer by 10 always equal the units digit Ignore all but the units digit and rephrase the question
What is the units digits of 317+713,
1) The pattern for the units digits of 3 in [3,9,7,1] every fourth term is the some. The 17th power is 1 past the end in 1,317 must end in 3.
2) The pattern for the units digit of 7 is [7,9,3,1]
every fourth term is the some. The 13th power is 1 part the end of the repeat since 712 ends in 1,713 must end in 7
Remainder when 1317+1713 is 3+7=10

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