# pairs

1. ### Modulus Problem

Choose three integer numbers x, y, and z = c, respectively, where x>=1, y>=1, and z >=1 to get (a, b) pairs. The condition is (1<=a<=x, 1<=b<=y) where [ (a + b) % c = 0 ] , a and b are integer numbers. Note: % is modulus For example: x = 10, y = 5, z = 2 answer = 25 pairs I will show a few...
2. ### No. of ways to divide 6 pairs into 3 teams so that no pairs are in the same team

There are 6 pairs (12 people) and they must be divided into 3 teams. All teams must have 1 or more occupants. Both people from a pair must not be in the same team. I already answered a similar question, the only difference was that there were two teams instead of three. If x is the number of...
3. ### Quuadratics whose real, irrational roots are NOT conjugate pairs

Quadratics whose real, irrational roots are NOT conjugate pairs Please bear with me as I'm not sure how to articulate this question succinctly. Often, when quadratic equations have real, irrational roots, they occur in conjugate pairs, but not always. (Contrast this with imaginary roots that...
4. ### Find the number of pairs (x,y) of positive integers which satisfy the equation x+2y=n

Let n be an odd integer >=5. 1) Find the number of pairs (x,y) of positive integers which satisfy the equation x+2y=n. 2) Find the number of triples (x,y,z) of positive integers which satisfy the equation x+y+2z=n. Anyone can help me? Thanks in advance.
5. ### Construct a calculus which produces exactly all pairs (S,t) such that var(t) = S

Construct a calculus which produces exactly all pairs $(S,t)$ such that $var(t) = S$ I have come up with the following rules: Define the rules of this calculus by, $\displaystyle{\over (\{\}, c)}$ where c:constant $\displaystyle {\over(S, x)}$ x:variable \$\displaystyle {x\,\,\, t_i...
6. ### Ordered Pairs & Vectors in ZFC?

About a week ago I asked Wolfram Alpha to find the power set of E = \{ \{ 1\} ,\{ 2\} ,\{ 2,3\} \} Here's what it gave me: \{ \emptyset ,(1),(2),(2,3),\{ \{ 1\} ,\{ 2,3\} \} ,\left( {\begin{array}{*{20}{c}} 1\\ 2 \end{array}} \right),\{ \{ 2,3\} ,\{ 2\} \} ,\{ \{ 1\} ,\{ 2\} ,\{ 2,3\} \} \}...
7. ### positive integer ordered pairs (x,y,x)

Total no. of positive integer ordered pairs (x,y,z) in x\times y \times z = 120 My Try:: We can write x\times y \times z = 2^3 \times 3 \times 5 Which is equivalent as we have 3 different boxes namely x,y,z and we have 5 balls in which numbers prints as 2,2,2,3,5, Now we will form different...
8. ### How to find the ordered pairs when you only have Ax=By=C?

So um, my homework wants me to find the ordered pairs of the equation in the picture, but the lesson never went over how to do so. How do I find the ordered pairs of an equation in the form of Ax=By=C?
9. ### Combinatorics - choosing exactly k pairs from n

Hi. I have the following combinatoric problem (well it's actually a probability problem that need to be resolved using combinatorics): There are n pairs of shoes in the closet. 2m shoes are chosen from it randomly. (m<n) find the probability to get exactly k pairs. so this is what I'm...
10. ### List all the ordered pairs in the relation R = {(a, b) | a divides b}

List all the ordered pairs in the relation R = {(a, b) | a divides b} on the set {1, 2, 3, 4, 5, 6}. Why isn't every ordered pair combo of the set in the relation R? I thought every combo would be part of the relation. For example (2,3) is not in the relation. Why not?
11. ### Pairs of primes and Cardinalities of sets

For a pair of primes (p_0,p_1), let Condition A be the following: For all integers n>0, \mbox{card}\left( \left\{ p_{1-j}^i \in \mathbb{Z} / p_j^n \mathbb{Z} \mid i \in \mathbb{N} \right\} \right) = p_j^n-p_j^{n-1} for both j=0 and j=1. Let M be the set of all pairs of primes that satisfy...
12. ### Number of pairs with give GCD and LCM (proof)

Hello, I would like a proof for the following algorithm, please. In order to find the number of pairs with a given GCD (greatest common divisor) and LCM (least common multiple), I find the number n of prime factors in LCM/GCD. The number of pairs is equal to 2^n. Example: GCD=2 and LCM=120...
13. ### ordered pairs

list the order pairs in the relation R from A={0,1,2,3,4} to B={0,1,2,3},where (a,b)belongs to R if and only if a)a|b i dont understand how to find these ordered pairs when divide relation occur like a|b and also explain me how to find these ordered pairs
14. ### help me find the ordered pairs for (x,y)∈r if 3 divides x-y (relations)

i need to figure out relations, and to that we were taught to find ordered pairs and then put them in a matrix, and then i can determine if this equation is reflexive, stymeteric,antisymmertic and so. i don;t know how to figure out what the ordered pairs are though.
15. ### Counting/Pairs Game problem

There exists a game that two people can play against each other. The outcome is always a win for one person and a loss for the other person. If 6 people play a game against each other, there are 6*5/2 total matches played, but can someone shed light on the topic of individual W-L records in...
16. ### Factor pairs

How can finding the factor pairs of the constant in a trinomial help me factor the trinomial???
17. ### Proof By Induction: Infinitely many pairs of consecutive pprime-ish numbers

Call an integer pprime-ish if each of its prime factors occurs with power two or higher. Prove by induction that there are in finitely many pairs of consecutive pprime-ish positive integers. I know how to prove that there are infinitely number primes, but am unsure of how to prove this.
18. ### Arrange 248 people in pairs

There are 248 students in a class. In how many ways is it possible to pair the students, in two and two in a pair ?
19. ### Sets of ordered pairs

I'm having trouble with one part of a 4 part problem. Determine and sketch the set of ordered pairs (x,y) in RxR that satisfies the following: |xy|<=2 I'm not sure what form they want the answer in. I was able to (Hopefully) figure out the other3, but this one is confusing me. I am not...
20. ### help with kinds of angle pairs

i was absent for days due to sickness and we have a homework. i can't understand the book itself. please help me by explaining on how to get the answer to these questions.. thank you. this is the figure: these are the questions Line r intersects lines x and y 1. Give as many vertical angles as...