Problem 6 · 2015 Math Kangaroo
Easy
Number Theory
last-digit
What is the unit digit of \(2015^2 + 2015^0 + 2015^1 + 2015^5\)?
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Answer: C — 6
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Hint 1 of 2
Only the final digit of each power matters — and the base ends in 5.
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Hint 2 of 2
Any positive power of a number ending in 5 ends in 5; remember 2015⁰ = 1.
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Approach: track only the units digit
- 2015², 2015¹, 2015⁵ all end in 5 (any power of a ...5 number ends in 5).
- 2015⁰ = 1.
- Units sum: 5 + 1 + 5 + 5 = 16, which ends in 6.
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