Show-for-the-equation-a-n-b-2-1-where-n-gt-1-and-a-gt-2-are-any-natural-numbers-there-are-no-positive-integer-solutions-for-a-and-b-

Tinku Tara June 4, 2023 Number Theory 0 Comments

Question Number 120202 by bemath last updated on 30/Oct/20

Show for the equation a^n = b^2 −1 where n>1 and a>2 are any natural numbers , there are no positive integer solutions for a and b ?

$${Show}\:{for}\:{the}\:{equation}\:{a}^{{n}} \:=\:{b}^{\mathrm{2}} −\mathrm{1}\: \\ $$$${where}\:{n}>\mathrm{1}\:{and}\:{a}>\mathrm{2}\:{are}\:{any}\:{natural} \\ $$$${numbers}\:,\:{there}\:{are}\:{no}\:{positive}\:{integer} \\ $$$${solutions}\:{for}\:{a}\:{and}\:{b}\:? \\ $$

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Show-for-the-equation-a-n-b-2-1-where-n-gt-1-and-a-gt-2-are-any-natural-numbers-there-are-no-positive-integer-solutions-for-a-and-b-

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