Mathematics - 18 October 2007

Okay, so the proof of the fact that the value of (p-1)! mod p is always p-1 is below:

If p is prime, the numbers {1,2,....p-1} form a group under multiplication modulo p. So for each element a in this group, there is an element b such that ab is congruent to 1 mod p.

If a is congruent to b mod p, then a^2 is congruent to 1 (mod p). This means that a^2 - 1 = (a+1)(a-1) = 0 (mod p). Since p is prime, this means a is congruent to 1 or -1 mod p (which means a = 1 or a = p-1).

Okay, so my question is, how did they get this part:
"If a is congruent to b mod p, then a^2 is congruent to 1 (mod p)."

2007-10-18 04:56:41 · 2 answers · asked by 3545 2

it's for homework, thanks.

2007-10-18 04:53:43 · 10 answers · asked by Anonymous

Consider the sequence given by...

u1 = −0.3, un+1 = un + 0.7 (n = 1, 2, 3, . . .).

(i) State what type of sequence this is.

(ii) Write down the first four terms of the sequence.

(iii) Find a closed form for the sequence.

(iv) Use the closed form from part (iii) to find the value of n when un = 36.1.

would the answers be this :

(i) it is an arithmetic sequence

(ii) the final first four terms are -0.3, 0.40, 1.10, 1.80

(iii) the closed form is: un= -0.3 + (n-1) 0.7

(iv) n = 53

are this right ????

2007-10-18 04:52:51 · 4 answers · asked by Anonymous

2007-10-18 04:45:11 · 2 answers · asked by christiansareawesome 4

2+ 5/x =7

2007-10-18 04:38:59 · 7 answers · asked by Anonymous

1/x^2 + 3/y^2 - 5/2xy

2007-10-18 04:35:21 · 2 answers · asked by Anonymous

A shopper buys three oranges and five lemons for $10.26, while a second shopper buys four lemons and six oranges for $11.16. What is the price of each fruit?

2007-10-18 04:32:35 · 5 answers · asked by Snoopy Baby 1

Please.. and thank you!

2007-10-18 04:28:27 · 3 answers · asked by Anonymous

1) a boat can go 9 km downstream in 45 mins. and return upstream in an hour. find the speed of the boat in still water and the speed of the current

2) the total time taken to travel x km at 30 km/h is 2 1/2 hours. the time taken to travel x km at 15 km/h and y km at 45km/h is 4 hour and 20 mins. find x and y

2007-10-18 04:14:20 · 2 answers · asked by javv>>> 2

Why do people must agonize themselves with Manual Computations? We are in a advanced technological era. Calculators (Scientific) are commonly used in the American land. Manual Computations slows down the process of computing in numerical algorithms and It is time-wasting. Calculators speeds up the process. Therefore the difference is not only in the difficulty in the process but in time. Time really matters. Would rather waste your neurons away or use it. What are your findings? Pls. try not to put answers that are baloney. What are your observations. Should we use machines or our brains? Skeptics are welcome.

2007-10-18 04:09:47 · 6 answers · asked by Kyle J 6

-Application of maxima and minima
1) A closed box with square base is to have a volume of 2000 in. The material for the top and the bottom of the box is to cost 3 cents per sq.in and the material for the sides is to cost 1.5 cents/in². Estimate to analytically the dimension of the box so that the total cost of the material is least.

2007-10-18 04:08:14 · 3 answers · asked by miaka 1

Thanks, I need this help for real. Algebra is not my strong point, I am struggling.

2007-10-18 04:07:09 · 4 answers · asked by ♥ ღAngelicaღ♥ 2

Solve |x| =1 (that's all it says)

How do I do this? I believe the answer is -1 and 1, but I need to explain how I got this answer.

2007-10-18 04:05:25 · 3 answers · asked by Anonymous

At work today, all five of us were left-handed. We thought that was odd and wondered the odds of that happening. Assuming the chances of one person left handed are 10%, I said the probability was 3.125%: Chances of selecting one person out five from a large population being left handed 50%, two 25% three 12.5% etc. Another person said it was much smaller .001%: .1^5. Who, if anyone, is correct?

2007-10-18 03:11:41 · 8 answers · asked by dishinki 2

In the first hour, they burrowed out 427 cubic inches of dirt. In the next hour, they burrowed out 256 cubic inches of dirt. In the third hour, they burrowed out 312 cubic inches of dirt. In the fourth hour, they burrowed out 546 cubic inches of dirt. In the fifth hour, they burrowed out 656 cubic inches of dirt. And in the sixth hour, they burrowed out 823 cubic inches of dirt. They continued for one more hour after that.

2007-10-18 03:03:49 · 2 answers · asked by kelly_h@verizon.net 1

a.

If today is Wednesday, then tomorrow is Thursday.
Hypothesis: Tomorrow is Thursday.
Conclusion: Today is not Wednesday.
b.

If today is Wednesday, then tomorrow is Thursday.
Hypothesis: Tomorrow is Thursday.
Conclusion: Today is Wednesday.
c.

Tomorrow is Friday if today is Wednesday.
Hypothesis: Today is Wednesday.
Conclusion: Tomorrow is Friday.
d.

Tomorrow is Thursday if today is Wednesday.
Hypothesis: Today is Wednesday.
Conclusion: Tomorrow is Thursday.

2007-10-18 03:00:00 · 4 answers · asked by Anonymous

I'm completely lost in my precalculus now. There was no school today and I have a test tomorrow and I was hoping that someone could explain how to find the real and complex zeros of the polynomial function below.

y = x^4 - 2x^3 + x^2 - 8x - 12

2007-10-18 02:37:44 · 8 answers · asked by majorzeb 1

Gasoline accounts for 85% of the motor fuel consumed in the U.S everyday. If 8882 thousand barrels (bbl) of motor fuel is consumed each day, how much gasoline, how much gasoline is consumed each day in the U.S. Round to the nearest barrel

2007-10-18 02:31:23 · 5 answers · asked by Nezbit 2

Find a 6-digit number which is a square of a number and cube of another, and when 6 is subtracted from it, it becomes a prime number.

2007-10-18 02:19:33 · 4 answers · asked by a 1

2007-10-18 02:05:21 · 5 answers · asked by Anonymous

2007-10-18 01:59:02 · 9 answers · asked by Anonymous

2007-10-18 01:33:06 · 1 answers · asked by dino 2

A 90% confidence interval around the variance was calculated. For n=27, the confidence interval was 35.0-88.4.

2007-10-18 01:30:22 · 1 answers · asked by scrappy1 1

(2xy^4e^y + 2xy^3 + y)dx + (x^2y^4e^y - x^2y^2-3x)dy = 0

2007-10-18 00:55:12 · 1 answers · asked by Mani 1

given cos (h) = summation notation symbol(0 to infinity) of x^(2n)/(2n)! for all x.

thanks a lot for the helping hand...

2007-10-18 00:53:52 · 1 answers · asked by Anonymous

6x^3dx + y^2(4y+9x^2)dy = 0

2007-10-18 00:53:17 · 1 answers · asked by Mani 1

(y+x^2y) dy/dx = 2x with y(0) = -2

2007-10-18 00:24:16 · 2 answers · asked by Mani 1

Please help with this too:

There exists a function f such that f(x) > 0, f'(x)<0 and f''(x)>0 for all real x. True or false?

Thanks a lot! :)

2007-10-18 00:20:33 · 5 answers · asked by Anonymous