examples, and problems from the community.

including olympiad champions, researchers, and professionals.

Number Theory
# Number Theory Warmups

examples, and problems from the community.

including olympiad champions, researchers, and professionals.

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What is the last digit of

\[ 123 \times 321 ? \]

**Hint:** There is no need to completely multiply these numbers.

examples, and problems from the community.

including olympiad champions, researchers, and professionals.

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by **Brilliant Staff**

What is the last digit of

\[ 123 + 321 ? \]

examples, and problems from the community.

including olympiad champions, researchers, and professionals.

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by **Brilliant Staff**

What is the last digit of

\[ 1 \times 3 \times 5 \times 7 \times 9 ? \]

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including olympiad champions, researchers, and professionals.

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by **Brilliant Staff**

What is the last digit of

\[ 1 \times 2 \times 3 \times 4 \times 5 \times 6 \times 7 \times 8 \times 9 ? \]

examples, and problems from the community.

including olympiad champions, researchers, and professionals.

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by **Brilliant Staff**

What is the last digit of

\[ 1234 \times 5678 ? \]

examples, and problems from the community.

including olympiad champions, researchers, and professionals.

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by **Brilliant Staff**

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