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Must a,b,c,d have the same sign?

Source: Baltic Way 2007

November 30, 2010
number theory proposednumber theory

Problem Statement

Let a,b,c,da,b,c,d be non-zero integers, such that the only quadruple of integers (x,y,z,t)(x, y, z, t) satisfying the equation ax2+by2+cz2+dt2=0ax^2+by^2+cz^2+dt^2=0 is x=y=z=t=0x=y=z=t=0. Does it follow that the numbers a,b,c,da,b,c,d have the same sign?
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