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for-m-n-positive-integers-m-gt-n-prove-that-lcd-m-n-lcd-m-1-n-1-gt-2mn-m-n-




Question Number 100677 by bobhans last updated on 28/Jun/20
for m,n positive integers m > n   prove that lcd(m,n) + lcd(m+1,n+1) > ((2mn)/( (√(m−n))))
$$\mathrm{for}\:\mathrm{m},\mathrm{n}\:\mathrm{positive}\:\mathrm{integers}\:\mathrm{m}\:>\:\mathrm{n}\: \\ $$$$\mathrm{prove}\:\mathrm{that}\:\mathrm{lcd}\left(\mathrm{m},\mathrm{n}\right)\:+\:\mathrm{lcd}\left(\mathrm{m}+\mathrm{1},\mathrm{n}+\mathrm{1}\right)\:>\:\frac{\mathrm{2mn}}{\:\sqrt{\mathrm{m}−\mathrm{n}}} \\ $$

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