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a+b = c+d = e+f = 101

Source: Polish MO Recond Round 1991 p3

September 9, 2024
number theory

Problem Statement

There are positive integers a a , b b , c c , d d , e e , f f such that a+b=c+d=e+f=101 a+b = c+d = e+f = 101 . Prove that the number acebdf \frac{ace}{bdf} cannot be written as a fraction mn \frac{m}{n} where m m , n n are positive integers with a sum less than 101 101 .
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