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course Mth 151
7/27 12
Question: `q001. There are seven questions in this assignment.Pick any even number--say, 28. It is believed that whatever even number you pick, as long as it is at least 6, you can express it as the sum of two odd prime numbers. For example, 28 = 11 + 17.
Express 28 as a some of two prime factors in a different way.
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Your solution:
5+23 which both are prime
3
Ok
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Question: `q002. The assertion that any even number greater than 4 can be expressed as a sum of two primes is called Goldbach's conjecture. Verify Goldbach's conjecture for the numbers 42 and 76.
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Your solution:
42 = 23 + 19, or 13 + 29, or 11 + 31, or 5 + 37.
76 = 73 + 3, 71 + 5, 59 + 17, 53 + 23, or 29 + 47.
3
Ok
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Question: `q003. The proper factors of a number are the factors of that number of which are less than the number itself. For example proper factors of 12 are 1, 2, 3, 4 and 6.
List the proper factors of 18 and determine whether the sum of those proper factors is greater than, less than, or equal to 18 itself.
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Your solution:
1,2,3,6,9
3
Ok
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Question: `q004. A number is set to be abundant if the sum of its proper factors is greater than the number. If the sum of the proper factors is less than the number than the number is said to be deficient. If the number is equal to the sum of its proper factors, the number is said to be perfect.
Determine whether each of the following is abundant, deficient or perfect: 12; 26; 16; 6.
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Your solution:
6 is perfect because 1,2,3 add up to 6
2
Ok
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Question: `q005. There is a perfect number between 20 and 30. Find it.
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Your solution:
28 because 1,2,4,7,14 add up to 28
2
Ok
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Question: `q006. Why can't a prime number be perfect?
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Your solution:
Because it only has 2 number it is divisible by 1 and itself
3
Ok
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Question: `q007. 2^2 - 1 = 3, which is prime. 2^3 - 1 = 7, which is prime. 2^5 - 1 = 31, which is prime. Is it true that for any n > 1, 2^n - 1 is prime?
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Your solution:
n = 4 you find that 2^n - 1 = 2^4 - 1 = 16 - 1 = 15, which is divisible by 3 and 5 and is not prime.
3
Ok
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