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lcm and gcd crossed square difference puzzle (Posted on 2024-09-22)

Determine all pairs (a,b) of positive integers that satisfy this equation:

lcm(a,b)² - gcd(a,b)² = 48

No Solution Yet Submitted by K Sengupta

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computer exploration

| Comment 1 of 4

for a=1:2000

for b=a+1:2000

if lcm(a,b)^2-gcd(a,b)^2==48

disp([a,b])

end

finds only

(1, 7) and (4, 8)

Of course their reversals are also solutions, and this does not guarantee completeness.

Posted by Charlie on 2024-09-22 08:20:24

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