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What an Odd Fact(or)

Can you show that 1^99 + 2^99 + 3^99 + 4^99 + 5^99 is divisible by 5?

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Lastly - Well

What are the last two digits of 2^(2^2003)?

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Diggits

Can you find what the last two digits of the number $4^{1999}$ are?