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Find all H.P.s with conditions

Source: (Indian) RMO 2008 Problem 5

November 9, 2008

number theory unsolvednumber theory

Problem Statement

Three nonzero real numbers

a,b,c

are said to be in harmonic progression if \frac {1}{a} \plus{} \frac {1}{c} \equal{} \frac {2}{b}. Find all three term harmonic progressions

a,b,c

of strictly increasing positive integers in which a \equal{} 20 and

b

divides

c

. [17 points out of 100 for the 6 problems]