divisible?

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

4 Answers

39
Dr.House ·

show your working...

1
Maths Musing ·

As 22000 and 2003m are coprime to each other ,

so 2003φ(p) = 1 ( mod 22000 )

now φ(p) = 22000 ( 1 - 1 / 2 ) = 21999

so m = φ(p) = 21999

1
Maths Musing ·

Err , can anybody confirm what I did ?

341
Hari Shankar ·

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

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