Two great mathematicians who have contributed greatly in the field of modular arithmetic are Swiss physicist Leonhard Euler and German child prodigy Carl Friedrich Gauss. They discussed the idea of congruence in great detail. Two integers are congruent modulo n if they yield the same remainder when divided by n. Which of the following pairs is congruent modulo 5? * 11 and 12 6 and 12 7 and 12 6 and 7

Q: Any number n is congruent to the sum of its digits modulo 4. Select one: True False

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Q: How would I solve for n and m (without a calculator)? Please explain. 5" = 3( mod 97) 5m = 7( mod…

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Q: how do you find "In (5/2) " on a calcualtor

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Q: 8. How many positive divisors does 2000= (2^4)(5^3) have?

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Q: Which pairs of the integers -11, -8, -7, -1, 0, 3, and 17 are congruent modulo 7?

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Q: 1. Show, using modular arithmetic, that for all n e N, 3(73") + 2"+3 is divisible by 11.

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Q: Determine the remainder of 102020 modulo 2020 and the remainder of 102020 modulo 2021.

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Q: The value of 2*5 where is defined as Modulo 7 is? 2. 3 3 4. 2

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Q: If 3x = 6 mod 9, when -2 <x< 8. Then O x=(-1, 3, 5} x=(-1, 2, 5} O x=(-1, 2, 3} O x=(-1, 5, 6}

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Q: Construct the addition and multiplication table for Z4 (Note that, both operations are mod4)

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Q: If 3x = 6 mod 9, when -2 < x< 8. Then O x={-1, 3, 5} x-1, 2, 5} O x=(-1, 2, 3} O x=(-1, 5, 6}

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Q: Solve the following. Show your solution. 1. How is modular arithmetic like a clock? If it is 16…

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Q: If a = 3 (mod12) then a does not equal 1 (mod6)

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