Pairs of a cubic

Number Theory Level pending

Determine all the pairs of ( x , y ) (x,y) of positive integers such that:

7 x 2 − 13 x y + 7 y 2 3 = ∣ x − y ∣ + 1 \Large{ \sqrt [ 3 ]{ 7{ x }^{ 2 }-13xy+7{ y }^{ 2 } } =|x-y|+1}

0 0 \2 \2 5 5 ∞ \infty None of these 17 17 1 1 12 12

Department 8 by Department 8 , 27, Israel

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