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If-a-b-are-co-prime-natural-numbers-satisfying-a-2-b-a-b-3-and-b-1-is-a-prime-find-all-possible-values-of-a-b-Please-help-me-solve-this-




Question Number 187213 by anurup last updated on 14/Feb/23
If a,b are co-prime natural numbers satisfying  a^2  + b = (a−b)^3  and b+1 is a prime find all  possible values of (a, b).  Please help me solve this.
$$\mathrm{If}\:{a},{b}\:\mathrm{are}\:\mathrm{co}-\mathrm{prime}\:\mathrm{natural}\:\mathrm{numbers}\:\mathrm{satisfying} \\ $$$${a}^{\mathrm{2}} \:+\:{b}\:=\:\left({a}−{b}\right)^{\mathrm{3}} \:\mathrm{and}\:{b}+\mathrm{1}\:\mathrm{is}\:\mathrm{a}\:\mathrm{prime}\:\mathrm{find}\:\mathrm{all} \\ $$$$\mathrm{possible}\:\mathrm{values}\:\mathrm{of}\:\left({a},\:{b}\right). \\ $$$$\mathrm{Please}\:\mathrm{help}\:\mathrm{me}\:\mathrm{solve}\:\mathrm{this}. \\ $$$$ \\ $$

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