Arithmetic Definition and 471 Threads

Homework Statement http://img264.imageshack.us/img264/7505/math.png Homework Equations AM = arithmetic mean = (a+b)/2 GM = geometric mean = sqrt(ab) The Attempt at a Solution I'm totally stuck on this, substituting does not help at all.

a few questions ... 25. Write an equation to show how the amount of money in a jar of nickels is related to the number of nickels in the jar. If the jar contains 40 nickels, how much money is this? (Hint: Define the variables that are used in your equation. Use your equation to to determine...

Homework Statement \mbox{Prove or give a counterexample: If p is a prime integer, then for all integers x and y, } (x+p)^p \equiv_p x^p+y^p. Homework Equations \equiv_p \mbox{just means (mod p). Can you please check and see if this proof is well-formed?} The Attempt at a Solution...

Homework Statement Show that the natural numbers satisfy commutativity of multiplication and distributivity of multiplication over addition. Homework Equations The Attempt at a Solution I'm wondering if there is any potential circularity in this reasoning. I proved distributivity...

Homework Statement If the sequence {a_n} n=1 to infinity converges to (a) with a_n >0 show {sqrt(a_n)} converges to sqrt(a) Homework Equations hint: conjigate first The Attempt at a Solution abs[ (a_n-a) / (sqrt(a_n)+sqrt(a) ) ] < epsilon i do not own LATEX, yet.

Am I correct in assuming that you can make sense of \infty + \infty and \infty + c for any c\in \mathbb{R} (both evaluate to \infty), but that we can make no sense of \infty - \infty? Are there any other arithmetic operations one can perform with infinities that are undefined?

Problem number 4 on the image has me stumped. I understand the problem (obviously not enough) and what its saying, I'm just having trouble putting it into a proof. Can i get a hint to get me started? Thanks http://img40.imageshack.us/i/asdasdjql.jpg/"

I got curious about RSA Encryption after the software signing key for TI-83s got cracked earlier this week and so I'm reading the wiki article about it[RSA]. I'm curious about a step so I'll fill in everyone and then highlight the step I'm not sure about. Key generation: 1. pick 2 prime...

Homework Statement A third degree polynomial has 3 roots that, when arranged in ascending order, form an arithmetic progression in which the sum of the 3 roots equal 9/5. The difference between the square of the greatest root and the smallest root is 24/5 Given that the coefficient of the...

Homework Statement Okay, so I'm going to find the smallest positive remainder of (21999+31998+51997) divided by seven. Homework Equations The Attempt at a Solution Well, I did like this: 23 is congruent to 1 (mod 7). Therefore, 21999= (23)1999/3 is congruent to 1 (mod 7). 33 is...

I was doing some conversions from binary to decimal and vice versa today using Windows Calculator and I noticed the following, if I multiply B11111111 and B11111111 I get the following: B1111111000000001. Uhhh...great! What's going on here? It looks like it's rolling over the 8 LSB when it...

Halfway through an undergraduate course in engineering, I'm now planning to review math fundamentals from pre-algebra, algebra, geometry to trigonometry and finally calculus because, as you may know, having a solid foundation in math is vital for any engineering course, and I've always been weak...

Arithmetic Sequences - PLEASE HELP! I would really appreciate any help to figure out the following 4 questions: 1) The Sum of the first two terms of an arithmetic progression is 18 and the sum of the first four terms is 52. Find the sum of the First eight terms 2) An arithmetic Progression...

Homework Statement 1. Prove that if ca=cb (mod m) and gcd(c,m)=1, then a=b (mod m) 2. Prove that if a=b (mod m), then gcd(a,m)=gcd(b,m)Homework Equations The Attempt at a Solution I can't figure out how to get started on these, especially the last one. Is it just a matter of expanding definitions?

Homework Statement prove that (a x b)^{}c = (a^{}c x b^{}c where a,b,c are any cardinal numbers Homework Equations The Attempt at a Solution i know that they should first be interpreted as sets A,B,C but what functions should I use.

Homework Statement The nth term of an arithmetic series is 1/2(3-n). What are the first three terms and the 20th term? Homework Equations nth term = a+(n-1)d The Attempt at a Solution I have made various attempts but cannot seem to work out how this can be done without a...

I have this formula: F = qVe + (Pe - Pa) * Ae; I want to get q by its self. This what I did to get q by its self. F = qVe + (Pe - Pa) * Ae \frac{F - (P_e - P_a)}{(A_e)} = \frac{(V_e * q)(A_e)}{(A_e)} [( F - (Pe - Pa)) ÷ Ae] ÷ Ve = q This is how I got q by itself in order to solve for...

Homework Statement An arithmetic progression has n terms and a common difference of d. Prove that the difference between the sum of the last k terms and the sum of the first k terms is | (n-k)kd |. Homework Equations \begin{array}{l} {S_n} = \frac{n}{2}\left[ {2{a_1} + \left( {n - 1}...

The sum of the first n terms in a certain arithmetic sequence is given by Sn = 3n2 - n. Show that the nth term of the sequence is given by an = 6n - 4. so far i have done: Sn = (n / 2) (a1 + an) = 3n2 - n i solved for a1 + an = 6n - 2 i also have an = a1 + d(n-1). i don't know what do...

The zeros of the polynomial f(x) = x^3 - 33x^2 + 354x + k form an arithmetic sequence. What is the value of k? so i let the zeros = a, b, and c. then i did b - a = c - b since it's an arithmetic sequence and they have common differences. so now i have a + c = 2b. i don't know what to do from...

Ten distinct prime numbers, each less than 3000, when arranged in increasing order of magnitude describe an arithmetic sequence. What are these ten prime numbers?

If the sum of the first 10 terms and the sum of the first 100 terms of a given arithmetic progression are 100 and 10, respectively, what is the sum of first 110 terms? S(10) = (10/2) (a1 + a10) = 100 S(100) = (100/2) (a1 + a100) = 10 a1 + a10 = 20 a1 + a100 = 0.20 a100 = a1 + 99d a10...

Homework Statement If n is composite, prove that there exist a,b in Zn such that a and be are nonzero, but ab=0 Homework Equations if a is congruent to b mod n, then n divides (a-b) The Attempt at a Solution So this is what i have so far, please let me know if i am on the right...

i might be making it up, but i am confused. can we say: x\equiv2 (mod k) x\equiv2 (mod m) hence x\equiv2 (mod km) by km i mean k multiplied by m. if not, what is the result? or can it be found? thank you in advance.

List all of the possible sums of prime number pairs with each element taken once. For instance: 2+3=5, 2+5=7, 3+5=8, 2+7=9, 3+7=10, 5+7=12, 5+11=16, 5+13=18 . . . Can you find significance in this progression? Have you seen this sequence before?

[SIZE="1"]Meta-note: This post includes both computer science and computational number theory. I could have posted it in the Programming forum, the CS forum, the NT forum, or here; I felt that this was the best place, especially since the CS forum does not actually deal with computer science...

i want to teach my boy arithmetic. my current 'best' idea, is to have a board with a few columns with nine spaces in each column. headings from right to left would be (units,tens, hundreds etc.). nine small plastic discs showing value of +1 unit. nine discs showing value +10 units. nine...

Homework Statement Prove if that if the limit of a_n = c as n approaches infinity, then the limit of o_n = c as n approaches infinity, where o_n is the arithmetic mean (a_1 + ... + a_n)/n Homework Equations I can't figure out how to bound it from below. The Attempt at a Solution...

Homework Statement find: 12^9 mod71 Homework Equations The Attempt at a Solution =12(12^8) mod71 = 12mod71 x 12^8mod71 = 12 x (12^2)^4mod 71 Now I'm stuck. My teacher solved it but i don't understand what he did so can someone explain how to do it in a very basic way...

Homework Statement Find x for ax = 1 (mod m) a) a = 15 , m = 31 b) a = 6, m = 93 c) a = 15, m = 20 if possible. (The equal sign above is equivalence in modular arithmetic) Homework Equations The Attempt at a Solution a) gcd(31,5) = gcd( 31 - 2*15, 15) = 1...

Homework Statement In an arithmetic progression, the sum of the first 10 terms is the same as the sum of the next 5 terms. Given that the first term is 12, find the sum of the first 15 terms. 2. The only one I could think of is S= n/2 (2a+(n-1)d) 3. I've tried solving it, but failed. I...

In tennis, the players switch sides after the odd games. one hot sunday the auther found himself on the side where he had begun the match a while earlier. He knew the game score was either 6-2, 4-3 or 6-2, 5-4. which was it? you must use modular arithmetic to solve this

Homework Statement Let m be a positive integer and m' be an integer obtained from m by rearranging its digits. Prove that m-m' is a multiple of 9 Homework Equations Casting out 9's method The Attempt at a Solution So I found that by applying the casting out 9's method on m and m'...

Homework Statement Let a, b, s, t be integers with s, t > 0. What conditions must s, t satisfy if the following statement is true: If a = b (mod s) and a = b (mod t), then a = b (mod st). The attempt at a solution If s | a, s | b, t | a and t | b, then st | a and st | b if and only if...

proof: n^2 congruent 0 or 1 (mod3) for any integer n

Howdy ho. No reason for a welcome around here, it's not about me it's about the Mathematical Anti-Telharsic Harfatum Septomin, eh!? (I hope at least one of you are familiar with that guy) Nonetheless, I've become obsessed with the transcendental property, and thusly therein my familiarization...

Homework Statement Show that if a = (b mod m) and c = d(mod m) and m => 2, then a - c = (b - d)(mod m) Homework Equations c = d(mod m) <=> m|(c - d) d = c + xm The Attempt at a Solution I don't know how any equivalences for a = (b mod m), is there a way to get b from a = (b mod...

Hello, What is the best way to determine direction, force, and velocity in three dimensional Cartesian coordinates? Explanation: I am writing a program to do some star motion simulations. I will edit in some stars, give them their mass, along with initial position and velocity, and see what...

Hey, (sin A + sin B + sin C)/3 >= \sqrt[3]{}(sin A*sin B*sin C) I know this is true by Arithmetic mean always greater than geometric mean... but is there any other way of proving this?

1) Suppose 2^k + 1 is a prime number. Prove that k has no prime divisors other than 2. (Hint: if k=ab with b odd, consider 2^k + 1 modulo 2^a +1) First of all, I have a little question. k=ab with b odd. Is this always possible for any natural number k? Why? Assuming it's always...

Arithmetic tables...?!? :confused: Any help would be v much appreciated!

C Program "Arithmetic Error" I'm writing a C program which prompts a user for an input decimal number (or any integer in base 10) as well as the n-base to which he wishes to convert the number to. However, for some reason my program failed to work and displayed "Arithmetic Error (core dumped"...

IMO, I don't really think arithmetic is really mathematics. It's just pure calculations, that's all.

I always thought that first order logic with identity was undecidable if it had either a 2-place relation or a 2-place function. Wikipedia seems to confirm what I'd thought: "The set of logical validities in any first-order signature with equality and either: a relation symbol of arity no less...

I'm working on a problem that involves calculating many discrete logarithms in GF(p): given n and an odd prime p, either find a k with 2^k\equiv n\pmod p or return "failure" if no such k exists. Now there are many algorithms for computing discrete logarithms, some of which are designed for many...

I have a solution to a problem which I am not certain that is complete. (It's a putnam problem so I can't believe I solved it) Would you mind to take a look at it? The problem stated: "Let A be any set of 20 distinct integers chosen from the arithmetic progression 1,4,7,...,100. Prove that...

Homework Statement I need to find all arithmetic sequences of integers with the property that the sum of the first n terms is a perfect square for all integers n. Homework Equations a_n = nth term of the sequence = a_1 + (n-1)d d = common difference Sum of the first n terms of the...

I'm trying to write a program which finds a solution to 2^k\equiv n\pmod p where p is an odd prime. At the moment I'm using a program like this: power = 2; exp = 1; while (power != n) { power = (2 * power) % p; // actually coded as an addition and conditional subtract if (power == 1)...

Find the limit of the following series: lim (n-->infinity) 1 + 3 + 5 + 7 + ... (2n-1) / (n+1) - [(2n+1)/2] 3. From what I kno this is an arithmetic series, meaning I must use that arithmetic series formula. so its (first term + last term / 2 times the number of terms) n^2.. now...

Homework Statement Compute: (a + b)^5 in Z_5 (Z mod 5). Homework Equations The end result is apparently: (a^5 + b^5) Intuition would tell me to exploit the properties of arithmetic in Z_n, however I don't see how I can reconcile this solution with just a normal expansion of (a+b)^5 (which...