For All Your Quant Queries
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Find the sum of all positive integers n such that x,y,z are positive factors of n-1, x>y>z and x+y+z=n
a) 13 b) 31 c) 44 d) 105 e) none of these
Written by Implex
August 27, 2008 at 12:41 pm
Posted in Number Thoery, Problem of the week
Tagged with Number Theory, Problem of the week
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factors are of the form (n-1)/2 , (n-1)/3 ,(n-1)/4, (n-1)/5….
They might be integer or not….but if integers they are the factors in descending order…
Highest possible sum= (n-1)/2 + (n-1)/3 + (n-1)/4 =13(n-1)/12 > (n-1)
Second highest = (n-1)/2 + (n-1)/3 + (n-1)/5= 31(n-1)/30
Next highest sum = (n-1)/2 + (n-1)/4 + (n-1)/5 = 19(n-1)/20 n=13
31(n-1)/30=n => n=31
hence sum 31+13=44
August 28, 2008 at 11:05 am
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