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## Homework Statement

i need to obtain the remainder of the divison [tex] 2^{1000005}[/tex] divided by 55

## Homework Equations

Euler theorem [tex] 2^{\phi (55)}=1 mod(55) [/tex]

## The Attempt at a Solution

my problem is that applying Euler theorem i reach to the conclusion that the remainder is the same as the value 'a' inside the congruence equation

[tex] 2^{5}=a mod(55)[/tex] but it would give me that a is negative ¡¡

it gives me a=-23 or similar using congruences or a =32