Suppose positive integers p,q,r are such that
pq = 32 and q = kČ/2
Then
p(kČ/2) = 32
pkČ = 64
p = 64/kČ
There are 4 square numbers kČ which are factors of 64.
They are 1, 4, 16, and 64.
Since q must be half a square number, we can eliminate odd number 1.
So q can only be 2, 8, or 32
Therefore there are three solutions:
1. 2 is a factor of 32 and also 2 is half of 4 which is a square number, 22.
2. 8 is a factor of 32 and also 8 is half of 16 which is a square number, 42.
3. 32 is a factor of 32 and also 32 is half of 64 which is a square number, 82.
Edwin
