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Diophantine equation : (a^2,b^2)+(a,bc)+(b,ac)+(c,ab)=199.

Source: Tuymaada 2001, day 1, problem 2.

April 30, 2007

greatest common divisornumber theory proposednumber theory

Problem Statement

Solve the equation

(a^{2},b^{2})+(a,bc)+(b,ac)+(c,ab)=199.

in positive integers. (Here

(x,y)

denotes the greatest common divisor of

x

and

y

.)
Proposed by S. Berlov