Geodesic
Equal values of trinomials revisited
Trudy Matematicheskogo Instituta imeni V.A. Steklova, Number theory, algebra, and analysis, Tome 276 (2012), pp. 255-261

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A necessary and sufficient condition is given for an equation $ax^m+bx^n+c=dy^p+ey^q$ to have infinitely many rational solutions with a bounded denominator, under the assumption that $m>n>0$, $p>q>0$, $ab\ne0\ne de$ and either $m>p>2$, or $m=p>2$ and $n\geq$. In a previous paper there was an additional assumption $(m,n)=(p,q)=1$. 
@article{TM_2012_276_a20,
     author = {A. Schinzel},
     title = {Equal values of trinomials revisited},
     journal = {Trudy Matematicheskogo Instituta imeni V.A. Steklova},
     pages = {255--261},
     publisher = {mathdoc},
     volume = {276},
     year = {2012},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/TM_2012_276_a20/}
}
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A. Schinzel. Equal values of trinomials revisited. Trudy Matematicheskogo Instituta imeni V.A. Steklova, Number theory, algebra, and analysis, Tome 276 (2012), pp. 255-261. http://geodesic.mathdoc.fr/item/TM_2012_276_a20/