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Omni-MATH / If a,b,c, and d are pairwise distinct positive integers that satisfy …anda+b=c+d,computethelargestpossiblevalueofa+b…

Problem

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problem

If a,b,ca, b, c, and dd are pairwise distinct positive integers that satisfy \operatorname{lcm}(a, b, c, d)<1000and and a+b=c+d,computethelargestpossiblevalueof, compute the largest possible value of a+b$.
Plain-text mathematical notation (without MathML)
If a,b,c, and d are pairwise distinct positive integers that satisfy \operatorname{lcm}(a, b, c, d)<1000anda+b=c+d,computethelargestpossiblevalueofa+b$.
Original LaTeX notation
If $a, b, c$, and $d$ are pairwise distinct positive integers that satisfy \operatorname{lcm}(a, b, c, d)<1000$ and $a+b=c+d$, compute the largest possible value of $a+b$.

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