Arithmetic Definition and 479 Threads

Homework Statement The sum of first three numbers of the arithmetic sequence is 54. If you subtract 3 from the first one, leave the second one unchanged and add 12 to the third one you get the first three numbers of the geometric sequence of the form ##ar + ar^2 + ar^3 + ... ar^n ## Find r...

Would it be possible to write an equation utilizing a summation of a modular function of a Cartesian function, whose degree is dependent upon the index of the root, in that it predicts the digits less than 1 of the root, that when summed equals the computed value sqrt( n )? I already have what...

I was very excited to learn that you can download the entire Trachtenberg Speed System of Arithmetic book for free from this website. (https://archive.org/details/TheTrachtenbergSpeedSystemOfBasicMathematics_201803) Why spend such an inordinate amount of time on arithmetic? Don't we have...

Good day, I'm working with a FORTRAN program that has the line: EDEN=EDEN+(STVS**2)/(N(J)-1) I would like to check if N(J)-1 is equal to zero. If so make N(J)-1=1.0 The following doesn't work: IF ((N(J)-1).EQ.0.0) THEN N(J)-1=1.0 END IF I'm using gfortran and am getting...

Homework Statement johns father gave him a loan of $1080 to buy a car. the loan was to repaid in 12 monthly installments starting with an intial payment of $p in the 1st month. there is no interest charged on the loan but the installments increase by $60/month. a) show that p = 570 and find in...

Good day. My FORTRAN program is throwing an ARITHMETIC exception on this line of code: SAREA(2,ISN)=SAREA(2,ISN)/IND(13)/1000./6080.2*IND(12)/1000. When I check this using gdb and print the contents of the variable SAREA(2,ISN), the value is 1432. gdb error message: Program received signal...

I have been doing research on entropy encoding for some time.. I found some interesting relationships between Arithmetic coding and other methods such as Huffman Coding. I made an article to explain them and am presenting here for review: http://siara.cc/arithmetic_coding_new_approach/ I have...

Homework Statement Three charged particles are placed at each of three corners of an equilateral triangle whose sides are of length 2.7 cm . Two of the particles have a negative charge: q1 = -6.0 nC and q2 = -12.0 nC. The remaining particle has a positive charge, q3= 8.0 nC . What is the net...

I have just received some help from Euge regarding the proof of part of the Correspondence Theorem (Lattice Isomorphism Theorem) for groups ... But Euge has made me realize that I do not understand quotient groups well enough ... here is the issue coming from Euge's post ... We are to consider...

Hi All, I am looking for the best way to learn math from elementary algebra (just above arithmetic) to calculus. I am looking for the most *comprehensive* way to do this--that is, I want continuity from subject to subject, for instance, a series of textbooks from a single author on Algebra I...

The state of arithmetic today is disgusting. The textbooks on it are absolutely repelling, the authors treat it like a subject that will be of concern to only babies. They don't show any love, they treat the subject like a dirty rug. It's been two years since I majored in mathematics, since...

Homework Statement The first term of an a.p is -8, the ratio of the 7th term to the 9th term is 5:8. what is the common difference of the progression? Homework EquationsThe Attempt at a Solution I've tried... it confuses me. Can anyone give me some hints or tips...?

There is a crucial bug on both WolframAlpha and Mathematica. When we give the input "Floor(sqrt(11.44-10)/0.2)" it gives wrong answer. The actual answer is six (6) but wolframalpha gives five (5). The problem is Wolframalpha calculates 11.44-10 incorrectly. Although the answer is exactly 1.44...

Homework Statement What is the greatest common divisor of ##X^a - 1 ## and ## X^b - 1 ##, ##(a,b) \in \mathbb{N}^\star## ? Homework EquationsThe Attempt at a Solution Assuming that ## a\le b ##, I find by euclidian division of ##b## by ##a## that ## b = an + r \Rightarrow X^b - 1 = (X^a-1)...

Homework Statement We are given ##a_1,...,a_n ## in ## \mathbb{N}^\star ##, all mutually prime, and ## a = a_1 \times ... \times a_n ##. Show that for all ##(b_1,...,b_n)\in\mathbb{Z}^n##, there is ##\beta \in \mathbb{Z} ## such that for all ##x \in \mathbb{Z} ## : ## (\forall i = 1 ... n, \...

This is an elementary question that I may blush about later, but for now: given that a recursively enumerable set is a set modeling a Σ01 sentence, and a recursive set is a recursively enumerable set S whose complement ℕ\S is also recursively enumerable. Fine. But then, letting x→ = the...

Hi everybody, I was doing one asignment form class, I was tasked to prove that in one system, the arimetic mean of FD and BE distributions is equal to MB's distribution for undishtingable particles. After doing the numbers I found out that it actually was, but I don't know why this happens, can...

Hey all, I was writing this program just now and wondered whether it would be easier for the cpu if I stored a number before I divided it by 2 or if i multiplied by 2 later to get that number back, I know it won't affect speed at all really but was just wondering, Any help appreciated.

The sum of the first 100 terms of an arithmetic progression is 15050; the first, third and eleventh terms of this progression are three consecutive terms of a geometric progression. Find the first term, a and the non-zero common difference, d, of the arithmetic progression.

Hey PF! Is there a systematic way to calculate the inverse of a number in a modular setting (modular setting? is that what I call it? lol). How about 108x == 1 (mod 625), wolfram alpha calculated x = 272, how could I have arrived at this number besides guess and check?

Hi, I am trying to find the current of a circuit using mesh analysis so far I have; My voltages V1 = 415 ∠ 90° or 0 + j415 V2 = 415 ∠ 0° or 415 + j0 impedances Z1 = j4 Z2 = j6 My formula is; -V1+Z1*I+Z2*I+V2=0 Which equates to; -0+j415+j4*I+j6*I+415+j0=0 Could...

Homework Statement Let ## a,b,c \in \mathbb{R}^{+} ##. Prove that $$ \sqrt[3]{abc} \leq \frac{a+b+c}{3}. $$ Note: ## a,b,c ## can be expressed as ## a = r^3, b = s^3, c = t^3 ## for ## r,s,t > 0##. Homework Equations ## P(a,b,c): a,b,c \in \mathbb{R}^{+} ## ## Q(a,b,c): \sqrt[3]{abc} \leq...

Hi there, I actually have a few questions I came across on my studies. They are (a) Show that if p is odd and x is an integer such that x^2 ≡ 1 mod p^k, then x = ±1 mod p^k (b) Find the solutions of the congruence equation x^2 ≡ 1 mod 2^k (c) What is the remainder of (p − 1)!, when divided by...

Hello I have a question reguarding human calculation. I'm in high school and I have been called a "math whiz" when it comes to subjects like algebra or calculus. But my school has kids using calculators so much that I haven't been using my head much for calculations. Because of this, I feel...

Homework Statement The ratio of sums of 2 AP for n terms each is ## \frac{3n + 8}{7n + 15}## that is $$ {\frac{s_a}{s_b}} = \frac{3n + 8}{7n + 15} $$ find the ratio of their 12th terms. $$ Required= \frac{a₁_a+(n-1)d_a}{a_b + (n-1)d_b}$$Homework Equations Tn = a + (n-1)dThe Attempt at a...

This is a self-assigned question. Not homework. I may have the right answer, but would like some reviewing. It came to me while reading on a CS topic, this did not come from a math textbook, otherwise it would be slightly more in context. I did not use any formula (so 2 would be empty) and 1...

I am actually quite sure I have it right but my book would then be wrong so I have posted my problem here to see if I didn't do a embarassing mistake in arithmetics. Homework Statement "Show that the energy equivalent of the length 10-18cm of a large extra dimension is roughly 20TeV" -Zwiebach...

Homework Statement I am required to find the units of ℤ8. Homework Equations I have that ##\bar{a}## = [a]n = { a + kn, k ∈ ℤ } ##u## ∈ ℤn is a unit if ##u## divides ##\bar{1}##. The Attempt at a Solution I'm not sure how to go about this. My lecturer wrote out the multiplication table...

Why is it significant enough to be fundamental? Some people say that it is fundamental because it establishes the importance of primes as the building blocks of positive integers, but I could just as easily 'build up' the positive integers just by simply iterating +1's starting from 0.

The roots of a fourth degree polynomial $g(x)=0$ are in an AP (arithmetic progression). Prove that the roots of $g'(x)=0$ must also form an AP.

Homework Statement Let X be a finite set and let x be an object which is not an element of X. Then X U {x} is finite and #(X U {x}) = #(X) + 1 The Attempt at a Solution Let X be a finite set such that X has cardinality n, denoted by #X. Suppose that ## x \notin X##, then the set X U {x} has...

1234567 ^ 7 ^ ~~1234567 5 & (12345678 ^ ~~ 12345678) My prof said there is an easy way to solve these as there is a trick to it. Does anyone know what trick is being referred to?

"Assume integer variable A holds 60 and variable B holds 13 then:A&B will give 12" Why is this?

In starting to look into the mathematical side of encryption , I note the heavy dependence upon modular arithmetic. What is the advantage is this? For example, why are finite cyclic groups and rings preferable? Note: I know zilch about programming; I am approaching it from the mathematical side.

3). A company is to distribute \$36,000 in bonuses to its top five sales people. The fifth salesperson on the list will receive \$6,000 and the difference in bonus money between successively ranked salespeople is to be constant. find the bonus for each salesperson. 4). Find the third term of...

1). Find the fourth term of the sequence of partial sums for the given sequence. {5+ 3\2 n} 2). A bicycle rider coasts downhill, traveling 7 feet the first second. In each succeeding second, the rider travels 6 feet farther than in the preceding second. If the rider reaches the bottom of the...

Need help on these questions I haven't been introduced yet. Please look at image I inserted in.

Homework Statement Of a 4 digit positive integer, the four digits form an Arithmetic progression from left to right. How many such 4 digit integers exist? 2. The attempt at a solution If d = 1, the integers are 1234, 2345, …, 6789. These 6 integers and their reverses satisfy the given...

I am looking for an arithmetic book to use before going on to pre-algebra. However I don't want a book that says "28 + 53, add 8 + 3, carry the 1, etc). I'm looking for a book that has a better approach. For example, instead of that approach, saying "28 + 53 = 30 + 51 = 81" - something like...

Homework Statement Determine whether there is a positive integer k so that the congruence is satisfied. 2k ≡ 1 (mod 11)Homework Equations gcd(2k,11) = 1The Attempt at a Solution Well, I know the answer is false. Because of Fermat's Little Theorem, 2k ≡ 2 (mod 11) But I'm not satisfied with...

Dear all, Please help me understand the proof by induction for only one way of expressing the product of primes up to the order of the factors. Please see the two attachments from the textbook "alan F beardon, algebra and geometry" A is a set of all natural numbers excluding 1 and 0?? r and s...

Homework Statement Hello! Please, take a look at the attached picture - there is a quote of the exercise and below is my attempt to make a matrix. Is my matrix correct? I have tried many times to convert it to inverse one, but I can't figure out how to do it - I keep getting "inconvenient"...

Homework Statement The binomial expansion of (1+x)^n, n is a positive integer, may be written in the form (1+x)^{n} = 1+c_{1}x+c_{2}x^{2}+c_{3}x^{3}+...c_{r}x^{r}+... Show that , if c_{s-1}, c_{s} and c_{s+1} are in arithmetic progression then (n-2s)^{2} =n+2 Homework Equations The Attempt...

I don't understand on how to get the answer of a certain problem in arithmetic series. formula/s: Arithmetic means An=A1+ (n-1)d Arithmetic series Sn=n/2 (A1+An) I understand on how to get the terms to these but when finding for: Find A1 if, S10= -20 , d= 4 & Find S12 if, 2+5+8+... I...

Hi, can't solve following prob: Let a, b and c be real numbers. Given that a^2, b^2 and c^2 are in arithmetic progression show that 1 / (b + c), 1 / (c + a) and 1 / (a + b) are also in arithmetic progression. From assumptions: b^2 = a^2 + nk and c^2 = b^2 + mk where k is some real number...

Homework Statement From an old exam: Show that \begin{equation*} \sum_{0 \leq 2k \leq n} \binom{n}{2k}2^k = 0 (3) \text{ iff } n = 2 (4). \end{equation*} By ##a = b (k)## I mean that ##a## is congruent to ##b## modulo ##k##. Homework Equations Binomial theorem: ## (a + b)^m =...

Homework Statement Hi, I am currently working on modular arithmetic and recently I have been investigating on the effects of exponentiation on the system.It will be helpful if someone can share some ideas on the following problem. According to the division algorithm: a= nQ+r, where a is the...

An arithmetic progression (AP) or arithmetic sequence is a sequence of numbers such that the difference between the consecutive terms is constant. Example: 2,4,6,8,10….. Arithmetic Series : The sum of the numbers in a finite arithmetic progression is called as Arithmetic series. Example...

Homework Statement Use 3-digit arithmetic with no pivoting to solve the following system: 10-3x-y=1, x+y=0. Homework Equations I know that 10-3=0.001. The Attempt at a Solution The answer for this problem is (0, -1). Here's the work: 1.001 0 1 1 I've...

Homework Statement Use exact arithmetic to solve the following system: 10-3x-y=1, x+y=0. Homework Equations I know that 10-3=0.001. The Attempt at a Solution Here's the work: y=-x 10-3x+x=1 x(10-3+1)=1 x=1/(0.001+1)=1/1.001 y=-1/1.001 since y=-x The answer for this...