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Oh i love these brain exercises! 
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#1
Jun2004, 02:36 PM

P: 95

if x and y are pos. int. then rx >=y. x is an int. help!



#2
Jun2004, 02:57 PM

Emeritus
Sci Advisor
PF Gold
P: 11,155

What is the question ?
If x, y are positive integers, there can always be found an r such that rx >= y. (Why repeat "x is an integer" ?) Do you want a proof of the above statement ? 


#3
Jun2004, 03:05 PM

Emeritus
Sci Advisor
PF Gold
P: 11,155

Assume that y > rx , for all r
Then the set S = {yrx r in Z+} consists only of positive numbers. So, S must possess a least element, say ymx. But y(m+1)x also belongs in S, since m+1 is in Z+ if m is. y(m+1)x = ymx  x < y  mx, since x>0, contrary to our choice of the minimal element  a contradiction ! Hence, the assumption was false. 


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