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[SPAM] Re: [obm-l] Inteiros!!!

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Ola Pedro e demais
colegas desta lista ... OBM-L,

Obviamente que todo par (X,Y) da forma (X,-X) e solucao, pois :
X^3 + (-X)^3 = 0 = (X+(-X))/2.  Em particular, (0,0) e solucao.

Se, porem, X+Y # 0, teremos :
X^3 + Y^3 = (X+Y)*(X^2 -XY + Y^2) = (X+Y)/2. => X^2 - XY + Y^2 = 1/2
=> (X-Y)^2 = - (X^2 +Y^2) .
A possibilidade aqui, logicamente, e :  X-Y=0 e X^2+Y^2 = 0. Mas isso
da (X,Y)=(0,0)
o que contraria a hipotese X+Y # 0

Assim, todas as solucoes inteiras sao {(X,-X) / X e inteiro }

Um Abracao a Todos
Paulo Santa Rita
6,0A2D,040408

2008/4/4 Pedro Júnior <pedromatematico06@xxxxxxxxx>:
> 02. Ache todos os pares tais de números inteiros (x, y) tais que:
> x^3 + y^3 = (x + y)^2

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