Assignment 24

course Mth 151

???????~~????Qv?j?assignment #024

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?w?????}??yO?????Liberal Arts Mathematics I

07-20-2006

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21:10:58

5.2.6 does 17 + 51 verify Goldbach for 68

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This is not true. 51 is not a prime, and both numbers must be prime.

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21:12:54

query 5.2.20 if 95 abundant or deficient?

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Ok to the explanation of number 6. I think I hit the next question button too many times.

Answer for number 20:

1 + 5 + 19 = 25

25 < 95

deficient

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21:13:00

**The proper factors of 95 are 1, 5 and 19.

These proper factors add up to 25.

Since the sum of the proper factors is less than 95, we say that 95 is deficient. **

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21:14:35

5.2.36 p prime and a, p rel prime then a^(p-1) - 1 div by p

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RESPONSE -->

3^(5-1) - 1= 80

80/5 = 16

2^(7-1) - 1 = 63

63/7 = 9

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21:14:56

** This result is verified for both a=3, p=5 and a=2, p=7:

If a = 3 and p = 5 then a and p have no common factors, so the conditions hold. We get a^((p-1))-1 = 3^(5-1) - 1 = 3^4 - 1 = 81 - 1 = 80.

This number is to be divisible by p, which is 5. We get 80 / 5 = 16, so in this case a^(p-1)-1 is divisible by p.

If a = 2 and p = 7 then a and p have no common factors, so the conditions hols. We get a^((p-1))-1 = 2^(7-1) - 1= 2^7 - 1 = 64 - 1 = 63.

This number is to be divisible by p, which is 7. We get 63 / 7 = 9, so in this case a^(p-1)-1 is again divisible by p. **

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21:16:46

query 5.2.42 does the nth perfect number have n digits?

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I don't think I understand what the ""nth"" perfect number means. I know that n stands for any number and I understand what n digits means, but I don't understand the first part.

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21:18:00

** The answer is 'no'. The first perfect number, 6, has one digit.

The second perfect number, 28, has 2 digits. So far so good.

The third perfect number is 496. Still OK.

The fourth is 8128, so we're still in good shape.

But the fifth perfect number is 33,550,336, which has 7 digits, so the pattern is broken.

The pattern never gets re-established. Note that the sixth perfect number has ten digits. **

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RESPONSE -->

OK - I get it now. I thought it meant the next perfect number and I haven't a clue about that. Once I see the answer I see how easy that was.

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Assignment 24

Good. Let me know if you have questions.