modulus

1. Modulus proof involving least positive residues

I'm a bit stuck on this question: Let p be a prime number. Prove that (2p−1)(2p−2)···(p + 1) ≡−1(mod p). Hint: ﬁnd the least positive residues of 2p−1,2p−2,...,p + 1 (modulo p). I think the least positive residues are {0,1,2,...,p} but not entirely sure, and I don't see how it's going to help...
2. Modulus Function Help

Sketch, on seperate diagrams, the graphs of y=|x|, y=|x-3|, y=|x-3| + |x-3|. Find the solution set of the equation |x-3| + |x-3| = 6
3. modulus (2)

it is a if and only if question 1<(4x-4)/(2x+3)<3 if 1<(4x-4)/(2x+3)<3 then |x+3/2|>5 2x+3<4x-4<6x+9 7<2x 4x-4<6x+9 7/2<x -13<2x 5<x+3/2 -13/2<x -5<x+3/2 then does it consider as |x+3/2|>5?
4. modulus

it is a if and only if type of question if |x-3|<|12x+5| then |x+13/3|>11/3 how do u guys solve this? my steps is as below (x-3)^2<(12x+5)^2 x^2-6x+9<144x^2+120x+25 0<143x^2+126x+25 and..... i get the wrong ans because it doesn't get |x+13/3|>11/3
5. modulus proving

prove that |x-y|=|y-x| for all x and y can we square both side for them ? then we get 2x=2y, x=y? B)|a+b|<_|a|+|b| to prove |x-y|>_ |x|-|y| how about this one ? my teacher gave me a hint that consider |x-y|+|y| how do we actually add two modulus together ? do we need to open up the modulus...
6. modulus of hermite polynomial

How to prove that |H_n(x)| \leq |H_n(ix)| where H_n(x) is the Hermite polynomial.
7. Modulus and inequalities question

Given |x-2| + |x-1|>1, how do I find the values of x that satisfy this equation? I know the normal way of solving this is to square both sides, but that doesn't seem to work in this case. Thank you!
8. cryptography maths

Dear all, been stuck at this problem for awhile. I am doing a cryptography implementation with the following equation: m + xr = m1 + xr1 mod q The objective is to solve r1 from this equation such that q is a prime number and m, r and x is an element of q with some help, i derive at: r1 = (m...
9. integral of modulus function

how to integrate |x*cos(Pi*x)| within the limits -1 to 1? I do not know how to proceed. kindly help me. Thanks with warm regards, Aranga
10. Solving a pattern regarding modulus

Hi everybody, i'm studying for my discrete math final next week and i'm having an issue with a certain problem. I have to solve this pattern regarding modulus: 5 8 56 45 23 34 67 2 3 3 3 5 4 23 4 5 5 ? ? ? ? (filling in the ?s) N = 3 I'm pretty sure I need to form a certain...
11. Probability question

Can someone give me a hint on how to calculate P(|Z|∈[3/2 ; 5/2])? Y(t)=tZ^2; t=4 Z~U(-2;2) U - continuous uniform distribution. Sorry for the images but I am new here and I thought it would be faster. Do you have any tutorials how to post maths symbols?
12. solve for x and y :modulus

|x-2|+|y+1|=0
13. solve for x; modulus inequalities

(a). -2|x-2|<-7 (b). |2x+1|>|-x+2|
14. modulus inequalitys

(a). -|-x - 2|>1 (b). 1<|x - 2|<3 (c). 6/|x+1|>/=3
15. modulus

-abs(x+1)+abs(1-x)=2 can anyone tell me how to solve this with a sound approach i dont have any clue what to start with abs is mod(modulus) answer is x is less than or equal to -1
16. modulus aka absolute value inequality

my attempt i squared both sides led me to 4x^2+20x+25 is greater than x^2+4x+4 3x^2+16x+21 is greater than 0 this lead to x is greater than -3 and less than -7/3 answer is x less than -3 and greater than -7/3
17. absolute Value aka modulus

mod(a+b) is greater than or equal to mod(mod(a)+mod(b)) i dont get it
18. Modulus

PLEASE FANS HELP ME OUT WITH THIS 3x + 11=13mod17
19. Modulus graph transformations

How would you draw the following graphs; Given f(x) = |x| a) y = 2 - f(x-1) Would it be the original modulus graph turned upside down (like a sharp n) and the top is point (1,2)? b) y = f(1-x) -1 Not too sure on this one :/ Cheers
20. complex number in polar form argument and modulus doubt

Pls share ur ideas i wish to knw were i have gone wrong or is the text answr is wrong pls help(Headbang)(Headbang)(Headbang)