what is the last 2 digits of 3 raised to 1994 and 7 raised to 1994??

Plz help me this is urgent :)

Printable View

- Aug 8th 2006, 09:45 PMxXxSANJIxXxCongruent numbers
what is the last 2 digits of 3 raised to 1994 and 7 raised to 1994??

Plz help me this is urgent :) - Aug 9th 2006, 07:34 AMSoroban
Hello, xXxSANJIxXx!

I found two different methods for these problems . . .

Quote:

What are the last 2 digits of ?

Since , consider the binomial expansion:

. .

. . . .

. . . . . . . . . These do not affect the last two digits

Therefore, the last two digits are: .

Quote:

What are the last 2 digits of ?

We note that:

. . Hence: will end in .

Since , we have: .

. . . . .

. . (a number ending in )

Therefore, the last two digits of are:

- Aug 9th 2006, 08:38 AMThePerfectHackerQuote:

Originally Posted by**xXxSANJIxXx**

Since,

you have,

To find, prime factorize 100,

Thus,

Thus,

Raise both sides to the 50th power,

Express as,

Let, then,

Solve for ,

- Aug 11th 2006, 02:50 AMxXxSANJIxXxTHx
Thank you guys... i kinda get it.... :confused: