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Erdős problem 443

Let m,n≥1m,n\geq 1. What is #{k(m−k):1≤k≤m/2}∩{l(n−l):1≤l≤n/2}?\# \{ k(m-k) : 1\leq k\leq m/2\} \cap \{ l(n-l) : 1\leq l\leq n/2\}? Is it ≤(mn)o(1)\leq (mn)^{o(1)} for all sufficiently large m,nm,n?

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sha256:1e660225fe777b67defe9413e503d7b309f2525729222789d1dcfa051eb86587
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sha256:58bb03f64fd5b6fdedde13917fbfee7e82dcf15b87060b7404cf9f454f3cabb8
Observation
sha256:8c823d621b7e1256c8e47c60a5f1c54c016a5507e6f27b2bab537f6f5f232067
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sha256:35f9645dc684a1aadd1d7abe3a1e32e9d698bac5933256eb73b0627a44e7f1ba
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sha256:c9d14c459c518937e758918b5897dc3b22f1a55f07739afe99502f5b046c907a
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2415f78e850aeee50afdca525c6f2e0ea606f207
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