course Mth 151 ?????????K?????assignment #024024. More number theory
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00:05:15 `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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RESPONSE --> 28 can be expressed as 5+23, both of which are prime #s confidence assessment: 2
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00:08:58 `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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RESPONSE --> 42 =23+19 or =13+29 or =11+31 or =5+37 76 =73+3 or =71+5 or =59+17 or =53+23 or =29+47 confidence assessment: 2
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00:09:50 `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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RESPONSE --> 1+2+3+6+9=21 its greater. confidence assessment: 2
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00:14:40 `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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RESPONSE --> 12: proper factors of 12 are 1,2,3,4,6 when added together = 16 this is abundant 26: proper factors of 26 are 1,2,13 when added together is 16 this is deficient 16: proper factors of 16 are 1,2,4,8 when added together is 15 this is deficient 6: proper factors of 6 are 1,2,3 when added together is 6 this is perfect confidence assessment: 3
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00:15:16 `q005. There is a perfect number between 20 and 30. Find it.
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RESPONSE --> 28 is perfect factors 1,2,4,7,14 confidence assessment: 2
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00:18:36 `q006. Why can't a prime number be perfect?
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RESPONSE --> the prime numbers have only two factors. the number and 1. the proper factor is the one true prime number that is greater then 1. A prime number cant be perfect. confidence assessment: 2
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00:19:15 `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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RESPONSE --> not prime confidence assessment: 2
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00:21:54 `q007. Check for p = 3, then p = 5, then p = 7 to see whether the formula 2^p - 1 seems to give primes.
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RESPONSE --> 2^3-1=8-1=7 2^5-1=32-1=31 2^7=1=128-1=127 all prime confidence assessment: 1
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??W??????????assignment #025 025. GCF, LCM Liberal Arts Mathematics I 12-14-2007
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00:27:25 `q001. There are three questions in this assignment. 2 * 2 * 3 * 5 = 60 and 3 * 5 * 7 = 105. What do the prime factorizations of 60 and 105 having common? What is the prime factorization of the smallest number which contains within its prime factorization the prime factorizations of both 60 and 105?
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RESPONSE --> they both have in common 3*5=15, the largest number that will divd evenly with both is 60&105 confidence assessment: 1
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00:30:54 `q002. What are the prime factorizations of 84 and 126, and how can they be used to find the greatest common divisor and the least common multiple of these two numbers?
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RESPONSE --> the prime factorizations of 84 is 2*2*3*7, and the prime factorizations of 126 is 2*3*3*7 The greatest common between the two is (2,3,7) 2*3*7=42 The least common is 2*2*3*7=252 confidence assessment: 2
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00:33:35 `q003. Find the greatest common divisor and least common multiple of 504 and 378.
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RESPONSE --> 504= 2*2*2*3*3*7 378= 2*3*3*3*7 the greatest common is 126, and the least common is 1512 confidence assessment: 2
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