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Show that 2abc-ab-bc-ca cannot be represented in such form

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October 5, 2010
number theory unsolvednumber theory

Problem Statement

Let a,b,ca, b, c be positive integers satisfying gcd⁡(a,b)=gcd⁡(b,c)=gcd⁡(c,a)=1\gcd (a, b) = \gcd (b, c) = \gcd (c, a) = 1. Show that 2abc−ab−bc−ca2abc-ab-bc-ca cannot be represented as bcx+cay+abzbcx+cay +abz with nonnegative integers x,y,z.x, y, z.
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