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find all 3 digit integers \overline{abc} = n so that 2n/3= a! b! c!

Source: Vietnamese MO (VMO) 1976 P4

August 20, 2018
number theoryIntegerinteger equationfactorial equation

Problem Statement

Find all three digit integers abc‾=n\overline{abc} = n, such that 2n3=a!b!c!\frac{2n}{3} = a! b! c!
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