Let-a-gt-b-gt-1-be-positive-integers-with-b-odd-Let-n-be-a-positive-integer-as-well-If-b-n-divides-a-n-1-prove-that-a-b-gt-3-n-n-Solution-please-Thanks-in-advance-

Tinku Tara June 4, 2023 Algebra 0 Comments

Question Number 31868 by 6123 last updated on 16/Mar/18

Let a>b>1 be positive integers with b odd. Let n be a positive integer as well. If b^n divides a^n −1, prove that a^b > (3^n /n). Solution please. Thanks in advance!!

$${Let}\:{a}>{b}>\mathrm{1}\:{be}\:{positive}\:{integers}\:{with}\:{b}\:{odd}. \\ $$$${Let}\:{n}\:{be}\:{a}\:{positive}\:{integer}\:{as}\:{well}.\:{If}\:\:{b}^{{n}} \:{divides} \\ $$$${a}^{{n}} −\mathrm{1},\:{prove}\:{that}\:{a}^{{b}} \:>\:\frac{\mathrm{3}^{{n}} }{{n}}. \\ $$$${Solution}\:{please}.\:{Thanks}\:{in}\:{advance}!! \\ $$

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Let-a-gt-b-gt-1-be-positive-integers-with-b-odd-Let-n-be-a-positive-integer-as-well-If-b-n-divides-a-n-1-prove-that-a-b-gt-3-n-n-Solution-please-Thanks-in-advance-

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