About the Diophantine Equation Y(Y+m1)(Y+m2)(Y+ m1+m2)=2X(X+m1)(X+m2)(X+ m1+m2)
Akbik, Safwan (2001) About the Diophantine Equation Y(Y+m1)(Y+m2)(Y+ m1+m2)=2X(X+m1)(X+m2)(X+ m1+m2). Safwan Akbik.
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Let m be the greatest common factor of the two positive integers m1 and m2. In this paper we show that if m has a "specific form," then the nontrivial solutions of the equation of the title are m times the "primitive solutions" of a similar equation with smaller m1 and m2. Also it is shown that the equation of the title with m1=1 and m2=3 has only four pairs of nontrivial solutions in integers given by X=14 or *18, and Y=17 or *21. Then we shall find all solutions in integers of the equation of the title if m2=3m1 and m1 is of a specific form.
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