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4 perfect squares

Source: CentroAmerican & Caribbean MO 1999 Q5

January 24, 2007

modular arithmeticnumber theory proposednumber theory

Problem Statement

Let

a

be an odd positive integer greater than 17 such that

3a-2

is a perfect square. Show that there exist distinct positive integers

b

and

c

such that

a+b,a+c,b+c

and

a+b+c

are four perfect squares.