Homework Help: Math

Posted by Anonymous on Saturday, October 13, 2012 at 10:55am.

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 - Reiny, Saturday, October 13, 2012 at 2:05pm
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

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