Modular Arithmetic (Medium)

Modular Arithmetic: core idea

• 1. Find the smallest positive integer $n$ with $n\equiv 2\pmod 5$ and $n\equiv 3\pmod 7$.

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• 2. Compute $2^{20}\bmod 13$.

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• 3. What is the last digit of $7^{2023}$?

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• 4. Compute $5^{100}\bmod 13$.

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• 5. Find the smallest positive $n$ with $n\equiv 4\pmod 6$ and $n\equiv 5\pmod 8$.

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• 6. Compute $6^{15}\bmod 17$.

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• 7. How many integers $1\le n\le 105$ are coprime to $105$?

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• 8. Find the modular inverse of $3$ modulo $11$.

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• 9. Compute $10^{50}\bmod 7$.

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