Problem 7 · 2023 Math Kangaroo
Medium
Number Theory
last-digitmod-10
What is the units digit of the following product? \((5^5+1)(5^{10}+1)(5^{15}+1)\)
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Answer: E — 6
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Hint 1 of 2
You only need the last digit of each factor.
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Hint 2 of 2
Any power of 5 ends in 5, so each factor ends in 6.
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Approach: track only units digits
- Every power of 5 ends in 5, so 55+1, 510+1 and 515+1 each end in 6.
- The units digit of 6·6·6 is the units digit of 216, namely 6.
- So the product ends in 6.
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