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              <text>¿Sabr´ ıa decidir el lector si existen n´umeros naturales (x,y) que satisfagan esta condici´on? Tenemos aqu´ ı un problema de planteamiento elemental cuya soluci´on no es nada f´acil. Si existiera un par as´ ı podr´ıamos tener suerte y encontrarloportanteo, perosinolohaynecesitaremosalg´untipoderazonamiento que lo justiﬁque, pues el no encontrar soluciones no signiﬁca que no las haya. Si el problema fuera x2 + xy + 3y2 = 15 el asunto ser´ ıa muy diferente, pues podr´ıamos hacer 4(x2 +xy+3y2) = (2x+y)2 +11y2 y de aqu´ ı sacar´ıamos una cota a las posibles soluciones, con lo que un n´umero ﬁnito de comprobaciones bastar´ ıa para decidir si las hay. Aun as´ ı habr´ıamos necesitado un peque˜no truco que requerir´ ıa un m´ınimo de perspicacia. </text>
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