All categories - 3 May 2007

2007-05-03 16:58:13 · 7 answers · asked by Phyllis C 1 in Other - Family & Relationships

1. Let p be a prime. Show that the equation x^2 'is congruent to' 1 mod p has exactly two solutions in Zp, 1 and p - 1.

2. Consider Z13 = {1, 2, ..., 12}. The elements 2, 3, ..., 11 can be paried off with their inverses as follows
(2, 7), (3, 9), (4, 10), (5, 8), (6, 11)
Problem : Generalize this example to the case where p is any prime and show that
(p - 1)! 'is congruent to' -1 mod p
(This result is called Wilson's theorem).

3. Show that if p is prime
(p - 1)(p - 2) ... (p - r) 'is congruent to' (-1)^(r) * r! mod p
for each r = 1, 2, ..., p - 1.

4. Show that if p is prime
2(p - 3)! + 1 'is congruent to' 0 mod p

5. In 1732, Euler wrote "I derived [certain] results from the elegant theorem, of whose truth I am certain, although I have no proof : a^(n) - b^(n) is divisible by the prime n + 1 if neither a nor b is."
Use Fermat's theorem to help Euler out with a proof.

Am completely confused about all the questions - please show working! Thx

2007-05-03 16:57:57 · 2 answers · asked by Oscar P 1 in Mathematics

2007-05-03 16:57:48 · 3 answers · asked by louann f 2 in Maintenance & Repairs

It's happened to me in a parking lot.

2007-05-03 16:57:37 · 14 answers · asked by Anonymous in Polls & Surveys

If you look at the statistics of those who are on welfare and receive government benefits over 3/4ths of them are natural born Americans who's families have been here at least 2 generations. Yet people want to blame immigration on the problems with our society.

2007-05-03 16:56:41 · 23 answers · asked by Anonymous in Immigration

Do you think it fell down from the sky, leather-bound and complete with Table of Contents (Canon)?

Did you know there is an Apocalipse of Peter that was read among the first Christians and that in the Councils of Hippo (393 AD) and Cartage (397 AD) St. Augustin argued that the Apocalipse of Jonh and not the one of Peter should be in the Bible and that is how you have it in your Bible now?

Hint: see what Luther said in his Commentary on St. John, chapter 16, “We are compelled to concede to the Papists that they have the Word of God, that we received it from them, and that without them, we should have no knowledge of it at all.”

2007-05-03 16:56:36 · 13 answers · asked by jemayen 2 in Religion & Spirituality

my molly is bloated and pregnant! I was told she gives live birth but i don't quite know if it's true??????

2007-05-03 16:56:35 · 7 answers · asked by Anonymous in Fish

2007-05-03 16:56:26 · 6 answers · asked by latania w 1 in Other - Health

2007-05-03 16:56:26 · 30 answers · asked by × 7 in Polls & Surveys

2007-05-03 16:56:19 · 8 answers · asked by davidxn 1 in Gambling

With the emergence of post modern thinking into religion as a form of escapism from the reality, can Christianity which is faith based survive?

2007-05-03 16:56:02 · 42 answers · asked by francen77 1 in Religion & Spirituality

i had mexican food 2 days in a row not taco bell good stuff you know but why wont the farts go away

2007-05-03 16:55:59 · 21 answers · asked by Anonymous in Etiquette

This is a story of two brothers who are tired of Mosquitoes. They decide to kill all the mosquitoes living in the pond near by the home. So they take out guns and walk towards the pond and when they reach near the pond , this brother sees a mosquito on other’s forehead , so this brother quickly aim the mosquito and pull the trigger and in result his brother died. Now he takes his brother’s dead body on his shoulder and starts walking back to home and when he reaches close to his home one of the neighbor asks what happened to your brother and he replies we went to kill our enemies and I killed one of the enemy and my brother died in friendly fire

2007-05-03 16:55:51 · 13 answers · asked by bright 3 in Military

from your contacts and had them tell you days after you kind of flipped out at the wrong person?

2007-05-03 16:55:50 · 6 answers · asked by comic book guy 5 in Polls & Surveys

2007-05-03 16:55:14 · 3 answers · asked by Ahab 5 in Religion & Spirituality

I'm in love with a man from 1/2 way across the country and I don't know what to do.
He could give me a nice life, minus my kids for the most time.
He is everything I have ever wanted.
My soul mate.
DO i run, and break some hearts, or stay, and keep all around me happy, and me not happy.
I want to be free to fly to him.
I want to see what life would be like with him.
What do you thinK?

2007-05-03 16:55:10 · 14 answers · asked by itmdjp 1 in Marriage & Divorce

Excluding God and Jesus.
Why?

2007-05-03 16:55:06 · 14 answers · asked by Lost. at. Sea. 7 in Religion & Spirituality

2007-05-03 16:54:45 · 17 answers · asked by TKDchikadee 2 in Religion & Spirituality

I need to hit the level with unlimited.

2007-05-03 16:54:35 · 29 answers · asked by Anonymous in Polls & Surveys

2007-05-03 16:54:22 · 9 answers · asked by Sparkles 7 in Other - Society & Culture

When the ISS (International Space Station) is completed what sort of things will it be capable of doing?

2007-05-03 16:54:14 · 4 answers · asked by Garrett B 2 in Astronomy & Space

why is it that the people who actually want to help the people around them as much as they can dont have the means to but the people that have the means to are selfish pigs?

2007-05-03 16:54:11 · 4 answers · asked by Mama Meg 1 in Other - Society & Culture

2007-05-03 16:53:58 · 17 answers · asked by Anonymous in Elections

2007-05-03 16:53:58 · 7 answers · asked by Joel H 1 in Tattoos

2007-05-03 16:53:57 · 10 answers · asked by Chase 4 in Polls & Surveys

What is the genotype of the mother?
What is the genotype of the fatther?
Using a Punnett square determine the population of the F1 generation.
What percentage of their boys will be colorblind?
What percentage of their girls will be colorblind?

Please simplify as best as you can on your answer, so I can understand it, I'm just learning Biology.
Thank you

2007-05-03 16:53:48 · 5 answers · asked by Kerri L B 1 in Biology

I'm seventeen & am 5'11 and want to work out my abs and muscles but I think I had read somewhere that working out too much can interrupt my growth process...Is that true?

2007-05-03 16:53:43 · 2 answers · asked by Miguel O 3 in Diet & Fitness

2007-05-03 16:53:37 · 3 answers · asked by Anonymous in Car Audio

one is left behind and the other vanishes.... without a trace.

2007-05-03 16:53:34 · 24 answers · asked by lucy02 6 in Polls & Surveys