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x-and-n-are-integers-p-is-a-prime-number-find-x-p-n-so-that-x-2020-3-p-n-




Question Number 135537 by metamorfose last updated on 13/Mar/21
x and n are integers  p is a prime number  find (x,p,n) so that : x^(2020) +3=p^n
$${x}\:{and}\:{n}\:{are}\:{integers} \\ $$$${p}\:{is}\:{a}\:{prime}\:{number} \\ $$$${find}\:\left({x},{p},{n}\right)\:{so}\:{that}\::\:{x}^{\mathrm{2020}} +\mathrm{3}={p}^{{n}} \\ $$
Answered by Olaf last updated on 14/Mar/21
If x = 0, p = 3 and n = 1  If x = 1, p = 2 and n = 2
$$\mathrm{If}\:{x}\:=\:\mathrm{0},\:{p}\:=\:\mathrm{3}\:\mathrm{and}\:{n}\:=\:\mathrm{1} \\ $$$$\mathrm{If}\:{x}\:=\:\mathrm{1},\:{p}\:=\:\mathrm{2}\:\mathrm{and}\:{n}\:=\:\mathrm{2} \\ $$

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