# integers

1. ### Solve for integers

2a+3b =5ab. Find all pairs (a,b) .:)
2. ### Pythagorean triple integers' occurrence

Is there a limit to how many times a particular integer may appear in different Pythagorean triples?
3. ### 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. ### Weird simple question on comparing positive and negative integers

Hi, I donÂ´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. ### Solve for integers

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

Solve the equation for n\in \mathbb{N} ; . 2n=2^n .
8. ### 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. ### 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. ### Subtract Integers 7 grade

I don't understand this problem because my teacher didn't explain it. 12-|8| Can someone explain?
11. ### 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. ### 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. ### 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. ### 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. ### Square rooting to gain negative integers

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

18. ### 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. ### 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. ### 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...