# Math

posted by .

Let a be an integer, then there are integers X, Y such that aX+(a+1)Y=1.

Find the smallest positive value of Y.

• Math -

aX + aY + a = 1
a((X+Y+1)=1
a = 1/(X+Y+1)
The only way that a can be an integer is for
X+Y+1 = 1 , to get 1/1
X = -Y

so X and Y must be opposite integers, and of course the smallest positive integer possible for X is 1

## Similar Questions

1. ### math, algebra

2a+2ab+2b I need a lot of help in this one. it says find two consecutive positive integers such that the sum of their square is 85. how would i do this one i have no clue i know what are positive integers.but i don't know how to figure …
2. ### Math

Find the smallest positive integer d such that d=105m+216n, where m & n are integers.
3. ### math

there are three consecutive positive integers such that the sum of the squares of the smallest two is 221. write and equation to find the three consecutive positive integers let x= the smallest integer
4. ### Math

Find the smallest positive integer n such that the equation 455x+1547y=50,000+n has a solution (x,y) where both x and y are integers

The smallest possible positive value of 1−[(1/w)+(1/x)+(1/y)+(1/z)] where w, x, y, z are odd positive integers, has the form a/b, where a,b are coprime positive integers. Find a+b.
6. ### Data Structures and Algorithms

Given integers R,M with M≠0, let S(R,M) denote the smallest positive integer x satisfying the congruence Rx≡1(mod M) if such an x exists. If such an x does not exist, put S(R,M)=0. Each line of this text file contains a …
7. ### la sallle

There are 3 consecutive even integers such that the quotient obtained by dividing twice the largest integer by the smallest integer is three less than three-fifths of the second integer. What are the integers?
8. ### Math

Find three consecutive even integers such that the sum of the smallest integer and twice the median integer is 20 more than the largest integer.
9. ### maths

the non- decreasing sequence of odd integers {a1, a2, a3, . . .} = {1,3,3,3,5,5,5,5,5,...} each positive odd integer k appears k times. it is a fact that there are integers b, c, and d such that, for all positive integers n, aĆ± = …
10. ### Algebra

Solve the following algebraically using one variable: Find three consecutive even integers such that the product of the smallest integer and the middle integer is eight less than eleven times the larger integer.

More Similar Questions