the integers are x,y,z
their reciprocals are [tex]\frac{1}{x}[/tex], [tex]\frac{1}{y}[/tex], and [tex]\frac{1}{z}[/tex]
the sum is 1
hmm
remember, a/a=1 when a=a
[tex]\frac{1}{x}+\frac{1}{y}+\frac{1}{z}=[/tex]
[tex]\frac{yz}{xyz}+\frac{xz}{xyz}+\frac{xy}{xyz}=[/tex]
[tex]\frac{yz+xz+xy}{xyz}=1[/tex]
therefor
yz+xz+xy=xyz
doesn't help much
different integers
ah, hum
the only way I can see is trial and error
find 1/x for x=2,3,4,5,6,7,8,9, etc and evaluate
1/2=0.5
1/3=0.3333
1/4=0.25
1/5=0.2
1/6=0.166666666
1/7=0.14285714285714285714285714285714
1/8=0.125
1/9=0.11111111111
1/10=0.1
1/11=0.090909090909090909
hum, experimentation tells us that it's probably not going to be 1/7
try adding the numbers and see which ones add to 1
hmm
ah ha
1/2+1/3+1/6=3/6+2/6+1/6=6/6=1
the integers are 2,3,6
their product is 2*3*6=36
