Problems
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8 problems
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1
Chinese Remainder Theorem Find the smallest positive integer x such that x β‘ 2 (mod 3), x β‘ 3 (mod 5), and x β‘ 2 (mod 7).
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Hard2Euler's Totient Function Compute Ο(12) , the number of integers from 1 to 12 that are coprime to 12.
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Medium3GCD Γ LCM Product Rule Given that gcd(12, 18) = 6, what is lcm(12, 18)?
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Easy4Modular Exponentiation What is the remainder when 3ΒΉβ°β° is divided by 7 ?
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Hard5Sum of Proper Divisors A perfect number equals the sum of its proper divisors. Is 28 a perfect number? Enter the sum of the proper divisors of 28.
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Easy6Number of Divisors of 360 How many positive divisors does 360 have?
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Medium7Divisibility by 9 What is the smallest positive integer d that can replace the blank in 4_72 so that the resulting four-digit number 4d72 is divisible by 9?
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Easy8Wilson's Theorem Application What is the remainder when 10! is divided by 11 ?
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Hard