Monday, May 13, 2019

number theory - Can sqrtn+sqrtm be rational if neither n,m are perfect squares?



Can the expression n+m be rational if neither n,mN are perfect squares? It doesn't seem likely, the only way that could happen is if for example m=an,  aQ, which I don't think is possible, but how to show it?


Answer



Squaring we get, m=a2+n2ann=a2+nm2a which is rational


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