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21 Oct 2009, 10:44
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How many integer pair for the below...
m=2n/(n-2)
//m,n are positive integer
steps please.
m=2n/(n-2)
//m,n are positive integer
steps please.
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21 Oct 2009, 12:13
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This is really good one.
NOTE:
A. n and m must be integers.
B. n>0 and m>0.
From B. --> m=2n/(n-2) --> clearly m to be positive n must be >2.
The same way: m=2n/(n-2) --> n=2m/(m-2) --> n to be positive m must be >2.
So we have m>2 and n>2
m=2n/(n-2) --> mn-2m=2n --> mn-2m-2n=0 --> mn-2m-2n+4-4=0 --> (m-2)(n-2)-4=0 --> (m-2)(n-2)=4
As m and n are positive integers >2 --> (m-2) and (n-2) also are positive integers --> 4 to be multiple of 2 positive integers only three pairs are possible: (1,4) (4,1) and (2,2)
m-2=1 and n-2=4 --> m=3, n=6
m-2=4 and n-2=1 --> m=6, n=3
m-2=2 and n-2=2 --> m=4, n=4
Answer: three pairs are possible (3,6) (6,3) and (2,2)
