Determine the tens digit of 3^1999. Could you find a second solution?

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- Nov 18th 2008, 04:56 AMbearej50tens digit
Determine the tens digit of 3^1999. Could you find a second solution?

- Nov 18th 2008, 09:16 AMo_O
Finding the remainder once divided by 100 will give you the tens and ones digits. For example, .

So the problem becomes:

By Fermat's theorem:

But:

So:

Raise both sides by 50 (the closest we'll get the power to 1999):

- Nov 18th 2008, 11:04 AMbearej50
thank you so much