Arithmetic Definition and 479 Threads

Homework Statement a) For which values of a does ax = 1 have a solution in Z5? b) For which values of a does ax = 1 have a solution in Z6? c) For which values of a and m does ax = 1 have a solution in Zm?Homework Equations None.The Attempt at a Solution Answers: a) All a ≠ 0 b) a = 1, 5 c)...

I was just curious. I believe the answer would be no, but I don;t know why

I have a homework problem and I use a rule to solve it that seems to be true, at least for small numbers, but I cannot seem to find a clearly stated theorem assuring me that it is true. Here's the problem with my solution: Find the remainder of the division of 2^(36!) by 37. Proof: By...

Homework Statement An arithmetic circuit has two select lines S1 and S2 and does the following arithmetic operations using a full adder: [function table] Determine the simplified Boolean functions for Xi and Yi for a single stage of the circuit given inputs A & B are n-bit registers...

.. This thread is intended to focus on arithmetic issues, mainly raised by JesseM, vanesch, DrChinese, ThomasT, in the context of: "What's wrong with this local realistic counter-example to Bell's theorem?" https://www.physicsforums.com/showthread.php?t=475076 : For newcomers to the issues...

Homework Statement Find some x such that x\equiv8 mod (18) Find the inverse of 12 modulo 41 Solve 2x=7 mod (13) Homework Equations The Attempt at a Solution I'm not sure how you do this. Can someone explain please? I know it's actually easy... but can't figure it out!

How do I solve those problems? Like, Find some x such that x\equiv8 mod (18) Find the inverse of 12 modulo 41 Solve 2x=7 mod (13) I know it's easy, but I don't get it. That's the explanation in the book. I'm not getting it. Can somebody please explain this modular arithmetic...

Finding log3(4) in Z(11).. Is that the same as finding log3(4)(mod11)?

Homework Statement Series Q is an arithmetic series such that the sum of its first n even terms is more than the sum of its first n odd terms by 4n. Find the common difference of the series Q. The answer provided is 4. Homework Equations The Attempt at a Solution I have no ideas on this...

Homework Statement Need help with number (9).. Homework Equations The Attempt at a Solution Can anyone give me some hints? Thanks.

Homework Statement Find the sum of the positive integers which are less than 150 and are not multiples of 5 or 7. Homework Equations The Attempt at a Solution I tried it... Can anyone give me some hints or tips...?

Homework Statement Solve the equation, if a solution exists: 3x = 4 (mod 6) Homework Equations If a = c (mod m), b = d (mod m), then: a * b = c * d (mod m) The Attempt at a Solution There is no solution, because 3x will always result in 0 or 3 for all integers x. However, what I...

I am having difficulty in understanding how the statement "7 + 5 = 12 " is a synthetic statement ? (I don't know whether this view is commonly accepted or whether opinion is divided on this issue.But I would like to know arguments put by those in favor of it.) I didn't have trouble in...

Hi I'm a layman so please keep your reply as simple as possible. Thanks. They say that a CPU has built-in circuitry to do simple arithmetic operations such as addition, subtraction, etc. and logical operation such as greater than, less than, etc. I don't understand how could some...

Beaconaut APICalc 2 just released on Jan.18, 2011, which is an arbitrary-precision integer calculator for bignum arithmetic, cryptography analysis and number theory research... http://www.beaconaut.com/forums/default.aspx?g=posts&t=13"

Homework Statement Corey has take a job with an initial salary of $26,000 an annual raises of $1,250/ (a) What will his salary be in the 6th year? (b) How much money in total will Corey have earned after six years? Homework Equations an = a1 + (n - 1) d Sn = n / 2 (a1 + an)...

Homework Statement For the arithmetic sequence (2 - x), (-6 + 2x), (x + 2), solve for x and find t10. Homework Equations an = a1 + (n - 1) d The Attempt at a Solution Would I have to start off like this below::: an = a1 + (n - 1) d d = (-6 + 2x)-(2 - x) = (x + 2)-(-6 + 2x)

I have a simple question: Why does 8^7 ≡ (-5)^7 (mod 13) and (25)^3 ≡ (-1)^3 (mod 13)? In essence I want to show that 8^7 + 5^7 = 13^7, so that both sides of the equation ≡ 0 (mod 13) and therefore 8^7 ≡ (-5)^7 (mod 13). I know that in a field of characteristic p>0, (x + y)^p = x^p +...

Homework Statement prove: lim x_n = L. Then \lim_{n\to\infty}\frac{x_1+\cdots+x_n}{n}=L Homework Equations The Attempt at a Solution i don't know abolutely. i tried definition \left|\frac{x_1+\cdots+x_n}{n}-L\right|=\frac{1}{n}\left|(x_1-L)+\cdots+(x_n-L)\right|

If the fourth, seventh and sixteenth terms of an AP are in geometric progression, the first six terms of the AP have a sum of 12, find the common difference of the AP and the common ratio of the GP. I've been assuming that the fourth, seventh and sixteenth terms of the AP are the fourth...

This isn't a homework question, it's in a textbook I have and I'm a bit stumped. I know there's something relatively simple I'm missing so any help would be much appreciated (working too). Three consecutive terms of an A.P. have a sum of 36 and a product of 1428. Find the three terms.

Homework Statement Calculate 7*11 + 9*11^-1 in the group Z20 Homework Equations The Attempt at a Solution 77+ (9*1/11) in group Z20 77 + 9/11 17 +11x= 20mod+9 My solution was 12, this makes 149 on both sides when you multiply the mod times 7. I am doing independent study...

Homework Statement Make four calculations in the group Z7 -------------------------------------------------------------------------------- First, calculate in Z7 6 - 3*5 = Homework Equations The Attempt at a Solution 6-15=6-1=5 =2 The program I am using...

Homework Statement let r_{1}, r_{2}, ... , r_{n} be strictly positive numbers. Suppose an investment of one dollar at the beginning of the year k grows to 1+r_{k} at the end of year k (so that r_{k} is the "return on investment" in year k). Then the value of an investment of one dollar at...

what is the maximum number of terms can a arithmetic progression of only prime numbers have?

Homework Statement When a is odd, show \frac{a^2-1}{8} is an integer. Then prove by induction n \geq 2 that for all odd numbers a_1,a_2,...,a_n, \frac{(a_1a_2...a_n)^2 - 1}{8} \equiv \frac{a^2_1 - 1}{8} + \frac{a^2_2 - 1}{8} + ... + \frac{a^2_n - 1}{8} \ mod \ 2 Homework Equations The Attempt...

Compute the following sums and give your answers in terms of n. (a) 1 + 2 + 3 + ... + n (b) 2 + 4 + 6 + ... + 2n (c) 1 + 3 + 5 + ... + (2n + 1) I actually have the answers but there seem to be an error... For (a) 1 + 2 + 3 + ... + n, My answer given is n(n+1)/2 For(b) 2 + 4 + 6...

Homework Statement The three number a, b, c, whose sum is 15, are successive terms of an geometric sequence, and b, a and c are successive terms of an arithmetic sequence. Find the values of a, b and c. Edit: I wrote the question wrong. It now reads correctly. I also fixed my latex code...

Homework Statement !( ((count<10) || (x<y)) && (count >=0) ) where count is equal to 0Homework Equations i don't think any equations here are necessary except maybe the precedence lawThe Attempt at a Solution they combined 'and' and 'or' which confused the heck out of me. How do i figure out...

Homework Statement (!) Assuming only arithmetic (not the quadratic formula or calculus), prove that \left\{x \in\Re: x^2-2x-3 < 0\right\} = \left\{x \in\Re: -1 < x < 3\right\} Homework Equations \left\{x \in\Re: x^2-2x-3 < 0\right\} = \left\{x \in\Re: -1 < x < 3\right\}...

Homework Statement Let a1, a2, a3 denote the first three terms of a geometrical sequence, for which a1 + a2 + a3 = 26. a1 + 3, a2 + 4, a3 - 3 are the first three terms of an arithmetical sequence. Find the first term and the common quotient (ratio) of the geometrical sequence...

So basically I am about to embark on my Msc in the pure maths department. Now I wish to conduct research on the subject of arithmetic quantum chaos and its applications in number theory and in gravity and cosmology. In my university I found someone who is an expert in its applications to...

I looked at a few modular arithmetic websites and I'm a neophyte when it comes to the legal operations/rules, syntax, and procedures of modular arithmetic. No GRE guide I've seen talks about modular arithmetic (not even the official one!). Following are five relevant questions from my GRE...

Homework Statement Theorem. (Fundamental Theorem of Arithmetic) Ever positive integer n has a prime factorization, which is unique except for reordering of the factors. Homework Equations 6.8 Definition. A prime factorization of n expresses n as a product of powers of distinct primes; the...

Homework Statement the first two terms in an arithmetic progression are 5 and 9. The last term in the progression is the only term which is greater than 200. Find the sum of all the terms in the progression Homework Equations The Attempt at a Solution I want to ask : what is the...

The raw data are lost, I have only final outputs (arithmetic means and standard deviations) for equally long measurement series. How I can compare results (calculate results) for the purpose to see significant statistic difference (significant difference, p<0.05)? Thank you in advance.

Homework Statement water fills a tank at a rate of 150 litres during the first hour, 350 litres during the second hour, 550 litres during the 3rd hour and so on. find the number of hours neccesary to fill a rectangular tank 16m x 7m x7mHomework Equations l=a+(n-1)d S= n/2 (a+l) where: l =...

Homework Statement A question gives the problem find the two arithmetic means between 4 and 19. The answer is 9 and 14. Homework Equations (a1+a2+a3+an)/n The Attempt at a Solution Logic would dictate that the arithmetic mean would be adding 4 and 19 then dividing by two. Leaving...

This is the question: What must fulfill a matrix to be invertible in module Zn? Demonstrate. Z refers to integers. I really appreciate that someone could help me with this because i couldn't find strong information about it. I think that considering A as a matrix... the det(A) must be coprime...

given any two numbers k,j what is the largest sequence of integers such that the sum of any k consecutive terms is negative and the sum of any j consecutive terms is positive and how may we find a subset containing k of the first n numbers such that out of all subsets with k elements, this...

Homework Statement Hi everyone. I'm studying a problem and I need to prove that I have a basis. I tryed a proof and to achieve it I need to show that : if k divides a*b and also divides a2 +2*b2 Then k divides both a and b. Homework Equations I'm not sure what I'm asserting is...

Homework Statement All the terms of the arithmetic progression u1,u2,u3...,un are positive. Use mathematical induction to prove that, for n>= 2, n is an element of all positive integers, [ 1/ (u1u2) ] + [ 1/ (u2u3) ] + [ 1/ (u3u4) ] + ... + [ 1/ (un-1un) ] = ( n - 1 ) / ( u1un)...

Homework Statement * note that I meant fields in the abstract mathematical sense, notphysical (i.e. electric) fields! * Finding the determinant of a matrix in GF(28) I want to know if it is using mod 256 or mod 255 in the field of GF(28) Homework Equations Just math The...

my book says that if sum of p terms of an ARTHMETRIC PROGRESSION is q and sum of q terms is p , then sum of p+q terms will be -(p+q) , but i am getting it as +(p+q), can someone verify it ?

Hi all, I was just wondering whether one could define arithmetic sequences in R^2 in a simmilar manner as in R.? Here is what i see as a natural way of doing it, but neither have i read about it, nor heard. \mbox{ Let } x_n \in R^2 \mbox{ be a sequence given as follows : } x_n=a+mb\\...

Homework Statement Using the Fundamental Theorem of Arithmetic, prove that every positive integer can be written uniquely as a power of 2 and an odd number. Homework Equations The Attempt at a Solution Since the FTOA states that any integer can be written as a product of primes...

"[URL consistency of ordinary arithmetic has not yet been satifactorily settled[/URL]. What is the upper limit for N such that arithmetic modulo N is known to be consistent?

Hi all, this (probably easy) problem from numerical analysis is giving me trouble. I can't seem to get started and need some poking in the right direction. Homework Statement Consider the following claim: if two floating point numbers x and y with the same sign differ by a factor of at...

Homework Statement Transmission of a quantum mechanical wave past a one-dimensional square well results in the following expressions relating initial to final wave amplitudes: A= (cos(2ka)-{i\epsilon\over2}sin(2ka))e^{2ia\lambda}F+{i\eta\over2}sin(2ka)G B=...

Homework Statement When finding the arithmetic mean in a system of equations is there any reason why the method that I am using is wrong? Find the arithmetic mean of x and y in the following set of equations Homework Equations 3x + 5y = 65 and 7x + 14y = 175 The Attempt at...