divisible?

find the least positive integer m such that 2²⁰⁰⁰ divides 2003^m-1

4 Answers

show your working...

As 2²⁰⁰⁰ and 2003^m are coprime to each other ,

so 2003^Ï†(p) = 1 ( mod 2²⁰⁰⁰ )

now Ï†(p) = 2²⁰⁰⁰ ( 1 - 1 / 2 ) = 2¹⁹⁹⁹

so m = Ï†(p) = 2¹⁹⁹⁹

Err , can anybody confirm what I did ?

341

Hari Shankar ·2010-01-15 18:37:10

from a lemma known as "lifting the exponent" m = 1998

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