MathDB

Given an integer

h > 1

. Let's call a positive common fraction (not necessarily irreducible) good if the sum of its numerator and denominator is equal to

h

. Let's say that a number

h

is remarkable if every positive common fraction whose denominator is less than

h

can be expressed in terms of good fractions (not necessarily various) using the operations of addition and subtraction. Prove that

h

is remarkable if and only if it is prime. (Recall that an common fraction has an integer numerator and a natural denominator.)

M2742