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1) How many zeros are there at the end of 1994!

[where n ! stands for n factorial]

2) Prove that if x1, x2, ...., x100 are distinct natural odd numbers

1/x1 + 1/x2 + ........ + 1/x100 < 2

3) Prove that if 'p' is a prime number then coefficients of the terms of (1+x)^(p-1) are alternately greater and less by unity than some multiples of 'p'.

4) Prove that 2222^5555 + 5555^2222 is divisible by 7.

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# Number theory questions

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