| Question: |
1 |
2 |
3 |
4 |
5 |
6 |
Total |
| Points: |
1 |
1 |
3 |
1 |
2 |
2 |
10 |
| Score: |
|
|
|
|
|
|
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1. (1 point) Use the Euclidean algorithm to find GCD(23,
17).
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2. (1 point) Suppose that x, y,m are integers, and 15x +
21y = z. What do you know
about z?
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3. (3 points) What is the exponent of 3 in the canonical
decomposition of 50!?
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4. (1 point) Suppose that x and y are integers. If GCD(x,
y) = 5, and LCM (x, y) = 210,
and x = 10, then what is y?
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5. (2 points) Suppose that N is a large integer. Do you think there are more
primes
between 1 and N, or between N and 2N? Justify your reasoning with the prime
number
theorem:
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6. (2 points) Suppose that a, b,
∈ Z, and a, b ≠ 0. Define precisely what it
means to say
that = LCM (a, b). In other words,
define the “ least common multiple ”.
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