1Yes, I think you will get 5 H.Ps
Three non-zero real numbers a,b,c are said to be in H.P. if 1/a + 1/c = 2/b. Find all three-term H.P. a,b,c of strictly increasing positive integers in which a = 20 and b divides c.
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2 Answers
62a = 20 and c=b.k
1/20 + 1/bk = 2/b
1/20 = 1/b(1-1/k) = 2(k-1)/bk
b=40(k-1)/k
k and k-1 are coprime!
so k is a factor of 40 .. so k is either 1,2,4, 5,8, or 10,20,40..
now we can easily remove the useless values..
i think we can reduce a few more calculations.. but this should suffice