integers

  1. I

    Solve for integers

    2a+3b =5ab. Find all pairs (a,b) .:)
  2. L

    Pythagorean triple integers' occurrence

    Is there a limit to how many times a particular integer may appear in different Pythagorean triples?
  3. L

    Close powers of integers

    Do there exist powers of integer pairs, both greater than three, whose differences are greater than two and singly sequential? For differences zero to two: 1^N-1^N=0...3^2-2^3=1...3^3-5^2=2... ?
  4. M

    Weird simple question on comparing positive and negative integers

    Hi, I don´t know how to deal with this: When comparing climate impact (contribution of CO2 released to atmosphere) of different types of insulation, how do I compare the positive and negative impact? I want to compare this materials: CORK -59 kg/m2 EPS +23 kg/m2 WOOL +96 kg/m2...
  5. I

    Solve for integers

    Find all pairs (x,y) such that x+y=xy , where $x,y$ are integers.
  6. R

    new symbol for negative integers

    Circling the negative number signifies that the amount is Owed because the amount is not produced until it is paid. A class at Umass spoke about this that I was in, but we may have spoke oppressively so this is to be certain people have the discussion if it was an idea that people incorrectly...
  7. I

    Solve for integers

    Solve the equation for n\in \mathbb{N} ; . 2n=2^n .
  8. J

    Why is the set of rational numbers dense, and set of integers numbers not?

    If we have two sets: Set one is the set of rational numbers with the usual less-than ordering Set two is the set of integers numbers with the usual less-than ordering Why is the set of rational numbers dense, and set of integers numbers not? Density is that for all choices of x and y with...
  9. J

    Sum of a non-decreasing sequence of integers

    For which pairs of positive integers $(n, d)$ is it true that every integer $S$ can be written as a sum of a non-decreasing sequence of integers $a_1+a_2+...+a_n$ and $a_n-a_1=d$?
  10. J

    Subtract Integers 7 grade

    I don't understand this problem because my teacher didn't explain it. 12-|8| Can someone explain?
  11. S

    Integral of the sum of all integers: -1/12

    The sum of all integers over the complex plane by analytic continuation is typically given as the Riemann zeta function evaluated at z({-1,0})=-1/12. But the partial sum at index 'n'' of the series is (n*(n-1)*)/2=n^2-x and looking at the definite integral S there we find that it's precisely...
  12. J

    combination of n integers, product not greater than x

    Hello here is my problem, I have n numbers, my multiplication combination can not involve more than 2 factors. How many products smaller than x will there be? Is there a function to determine that? Thank you.
  13. L

    Gaussian integers

    Pick up prime elements of the ring of Gaussian integers G = {a+ib/a,b \in R} from the following: A) 2 B) 3 C) 7 D) 13 My answers : Options B & C please check and let me know... Thanks. :)
  14. S

    Maths - Integers

    Dear Experts, Greetings! I need your guidance on the below Maths- Integer problem. Find the difference between the smallest positive integer and the greatest negative integer. I tried this way: the smallest positive integer = +1 the greatest negative integer = -1 Difference +1 -...
  15. Xxmarijnw

    Square rooting to gain negative integers

    Are there any (complex, real etc.) numbers that satisfy the following equation? \sqrt{x} < 0
  16. B

    Check if equation defines an operation on the set of integers.

    Hi, I have the following exercise, it is required to check if the following equation defines an operation on the set of integers, and if so, check if it is associative, commutative and identity element. $m * n = mn + 1$ I have taken $m = 2, n = 3$ $2*3 = (2 \cdot 3) + 1 = 6 + 1 = 7...
  17. B

    Each integer is congruent modulo n to precisely one of the integers 0,1,...,n-1.

    Hi, I have the following exercise: Choose n = 5, then [3] \oplus [4] = [3+4] = [7] = [2] END. I don't understand what is the passage that makes $[7] = [2]$ Why the set that contains the numbers that have remainders equal to 7 when divided by 5, is the same (contains the same elements), of the...
  18. ProofOfALifetime

    How are integers a subset of R^2?

    I am reading an Analysis book and it says, "Let us consider the following subsets of R^2" It goes on to mention these sets: The set of all integers The set consisting of the numbers \frac 1n for (n=1,2, 3,...) The segment (a,b) My question is, isn't this R^1? How is this R^2? It may seem...
  19. D

    Is there a way to find the positive integers with 4 factors less than 100?

    I know how to do the problem below in a tedious way. But I cannot think of an easier way to do it. (ex) Consider all the positive integers less than 100 that have exactly four factors which include 1 and the number itself. Find the sum of all these integers. The most obvious way is to list...
  20. L

    Factorial-summation ratio integers

    n..........n!.........................sum(n)..................n!/sum(n) 1..........1............................1.........................1 2..........2............................3 3..........6............................6..........................1 4..........24..........................10...