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bers Euclid (born approx. 300 BCE) discovered that the first four perfect numbers are generated by the formula (2P-1)(2P – 1), where P is prime. a.) The second part of this formula, (2P – 1), is a special kind of prime number, invented by a French monk, called a prime (sec. 2.1). b.) Show how you would use this formula (2P-1)(2P – 1)with P= 2. You should get the first perfect number, 6. Caution: in the first part, (2P-1), all of the P-1 is in the exponent. In the second part, (2P – 1), only the P is in the exponent. c.) Show how you know 6 is perfect by showing what its proper divisors add up to.

bers Euclid (born approx. 300 BCE) discovered that the first four perfect numbers are generated by the formula (2P-1)(2P – 1), where P is prime. a.) The second part of this formula, (2P – 1), is a special kind of prime number, invented by a French monk, called a prime (sec. 2.1). b.) Show how you would use this formula (2P-1)(2P – 1)with P= 2. You should get the first perfect number, 6. Caution: in the first part, (2P-1), all of the P-1 is in the exponent. In the second part, (2P – 1), only the P is in the exponent. c.) Show how you know 6 is perfect by showing what its proper divisors add up to.

Advanced Engineering Mathematics
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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ient and Abl ural number is deficient if it is greater than bundant if it is less than the sum of its proper divisors. lente her is one with proper divisors that add up to --is one with proper divisors that nner divisors of 8 Project 2: Number Patterns, p. 11 9. Perfect Numbers Euclid (born approx. 300 BCE) discovered that the first four perfect numbers are generated by the formula (2P-1)(2P – 1), where P is prime. a.) The second part of this formula, (2P – 1), is a special kind of prime number, invented by a French monk, called a prime (sec. 2.1). b.) Show how you would use this formula (2P-1)(2P – 1)with P= 2. You should get the first perfect number, 6. Caution: in the first part, (2P-1), all of the P-1 is in the exponent. In the second part, (2P – 1), only the P is in the exponent. c.) Show how you know 6 is perfect by showing what its proper divisors add up to. d.) Find the second perfect number using the formula (2P-1)(2P – 1)and the next prime number for P. (Do not use P = 4, since 4 is not prime). TIP: when you are done, you might do a web search for perfect numbers to see if you are right. wtar with sre e.) Show how you know this new number is perfect by showing what the proper divisors add up to. the f.) Find the third perfect number using the formula (2P-1)(2P – 1) and the next prime number for P. Show your work, not just your answer. g.) Use a prime factor tree to find all the prime factors of your new perfect number. This will help you find the proper divisors. FOlin Che blonks, aalng a inatnd of the the forule in the The la fon h.) Show how you know this new number is perfect by showing what the proper divisors add up to. thesome elants
Transcribed Image Text:ient and Abl ural number is deficient if it is greater than bundant if it is less than the sum of its proper divisors. lente her is one with proper divisors that add up to --is one with proper divisors that nner divisors of 8 Project 2: Number Patterns, p. 11 9. Perfect Numbers Euclid (born approx. 300 BCE) discovered that the first four perfect numbers are generated by the formula (2P-1)(2P – 1), where P is prime. a.) The second part of this formula, (2P – 1), is a special kind of prime number, invented by a French monk, called a prime (sec. 2.1). b.) Show how you would use this formula (2P-1)(2P – 1)with P= 2. You should get the first perfect number, 6. Caution: in the first part, (2P-1), all of the P-1 is in the exponent. In the second part, (2P – 1), only the P is in the exponent. c.) Show how you know 6 is perfect by showing what its proper divisors add up to. d.) Find the second perfect number using the formula (2P-1)(2P – 1)and the next prime number for P. (Do not use P = 4, since 4 is not prime). TIP: when you are done, you might do a web search for perfect numbers to see if you are right. wtar with sre e.) Show how you know this new number is perfect by showing what the proper divisors add up to. the f.) Find the third perfect number using the formula (2P-1)(2P – 1) and the next prime number for P. Show your work, not just your answer. g.) Use a prime factor tree to find all the prime factors of your new perfect number. This will help you find the proper divisors. FOlin Che blonks, aalng a inatnd of the the forule in the The la fon h.) Show how you know this new number is perfect by showing what the proper divisors add up to. thesome elants
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