SOLUTION: What is the remainder when 2^1024 + 5^1024 +1 is divided by 9?
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Question 549506: What is the remainder when 2^1024 + 5^1024 +1 is divided by 9?
Answer by richard1234(7193) (Show Source): You can put this solution on YOUR website!
Several ways to do this. One way is to that
)
, and that
 \equiv 2((-1)^{341}) \equiv 2(-1) \equiv 7)
(modulo 9).
Similarly,
(5^6)^{170} \equiv (5^4)(1^{170}) \equiv 5^4 \equiv 4)
(modulo 9).
Hence the sum is equivalent to 7 + 4 + 1 = 12 = 3 (modulo 9), so the remainder is 3.
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