# arithmetic

1. ### Ordinal Arithmetic (Exponentiation)

Hi, I've found a problem in Set theory that I can't really get my head around. The problem is: Under ordinal exponentiation find an ordinal \mu such that \omega < \mu and 2^{\mu } = \mu (where \omega is the inductive set of natural numbers and < is \in) I think the correct approach would be...
2. ### arithmetic

hello can someone please help me to solve this problem: 2008 mod 71, 92 mod 41, 342 mod 71 b)determine all a and b that verify a2 mod 41=40 b2 mod 71=20 this is my answer: a) 2008 mod 41=40 2008 mod 71=20 92 mod 41=40 342 mod 71=20 b) i noticed that a=9 is a solution for : a2 mod 41=40 and b=34...
3. ### need help with modular arithmetic and equivalence classes.

First problem Let n ∈ N and let Z denote the set of equivalence classes for the relation of congruence modulo n. Let n ∈ Z. Define the order of the element [a]n ∈ Z to be the smallest number k such that : k * [a]n := [a]n + [a]n+....+[a]n = [0]n where the number of terms in the sum is k. (a)...
4. ### need help solving proofs, modular arithmetic, and equivalence relations

attached 3 photos of questions I couldn't figure out. Would really appreciate some help especially with the proof involving a partition.
5. ### ln Arithmetic

Some problems with this in Calculus, as in partial fractions the definite integrals come down to this at the end. Let's say you have Case A A \ln (C) \pm A\ln (C) = 5\ln(1) - 5 \ln(1) = 5\ln(1) + 5 \ln(1) = Case B: A \ln (C) \pm B\ln (C) = 5\ln(1) - 4 \ln(1) = 5\ln(1) + 4 \ln(1) =...
6. ### Arithmetic Sequence Questions (!)

Hello, I am currently studying arithmetic sequences and series and have some questions. I know the formulas but am confused by what they mean and how they work and when to use each one. To find the sum of a certain number of terms of an arithmetic sequence, you use this formula: So here's...
7. ### Arithmetic Sequence

You have a gift card for a coffee shop worth $90. Each day you use the card to get a coffee for$ 4.10. Write a rule to represent the amount of money left on the card as an arithmetic sequence. What is the value of the card after buying 8 coffees?
8. ### Convert Sigma notation to the partial sum formula

75 Σ(2n-1) _______ I get 4,888 but when i put it into wolfram alpha it says the answer is 5,264 n=20
9. ### Train your mental arithmetic skills with Math Tower

Math Tower is an addictive math game! Compete with your friends and the world in the global ranking system (Talking) From easy addition and subtraction tasks to more advanced multiplication and division tasks and the combination of them all; exercise your BRAIN as you build experience and reach...
10. ### Numerical Analysis - Floating-point Arithmetic

Let f(x) = (x^2)*[sqrt(3 + x^2) - x] (a) If floating-point arithmetic is used to calculate the value of f(x) for large x-values, the result might not be satisfactory due to round-off error. Explain why. (b) Rewrite f(x) in a different form so that better approximation can be obtained. If...
11. ### Arithmetic or Geometric Sum?

A woman started a business with a workforce of 50 people. Every two weeks the number of people in the workforce increased by 3 people. Each member of the workforce earned \$600 per week. What was the total wage bill for this 26 weeks? So, the wage for the initial 50 is 50*26*600. Now for the...
12. ### Arithmetic mean

Compute arithmetic mean of the following distribution of marks in Economics of 50 students. Marks more than No. of Students 0 50 10 46 20 40 30 33 40...
13. ### exponentiation in modular arithmetic

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 dividend,n is the...
14. ### Two exercises - polynomial equations and geometric and arithmetic sequences

Hey, my neighbour again send me one exercise. 1. In the equation x^{3} - 7x^{2} - 21x + a = 0 you must find solutions whose are in geometric sequence. For which a? How can I find this a? 2. In the equation x^{4} -(a+3)x^2 + (a + 2) = 0 must find this a that solutions are in...
15. ### Some formulas of Arithmetic progression/series

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...
16. ### Arithmetic operations problem

Hi all, I wonder if you could let me know how to resolve c) and d) I could resolve a) and b) by factoring however don't know how to add the values inside the brackets in c) and d) (Thinking) Many thanks, Matilde
17. ### Modular Arithmetic

Is there a simple way to prove that ɸ(p) = p - 1 I would appreciate any suggestions
18. ### Modular Arithmetic

I need help with the following question please. Calculate 7^42 mod 150
19. ### Arithmetic Sequence

For a positive integer, consider the arithmetic sequence: n, n+19, n+38, n+57,....... The number 2013 may or may not belong to the sequence. What is the smallest positive integer n such that 2013 does belong to the sequence? A) 4 B) 7 C) 11...
20. ### Modular arithmetic

1/192 = k mod7 I ran this through Wolfram Alpha and got the answer k=5 I assume that this is because (192 * 5)/7 has a remainder of 1 (is this correct?) Is there a good way of finding the 5 manually? Thankyou.