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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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