Math CentralQuandaries & Queries


Subject: math
Name: Ryan
Who are you: Student

What is the units digit of the sum of 9^2006 and 3^2006


What you want to note is that when you take powers of 3 the units digits generate a sequence 3, 9, 7, 1, 3, 9, 7, 1, ...; so for example every fourth one is a 1 and 31000 would end in a 1 as 1000 = 250 x 4.

Your problem can be looked at as finding the units digit of 34012 + 32006 (why is that?). From what we've just said above the 34012 must end in a 1 now what about 32006?



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