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University Problem Solving Thread

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dcc:
Another Problem:

Find the smallest prime number which is a factor of:

Ahmad:
Solution
leaves a remainder when divided by all primes less than 99.

However, 99! - 1 has the same smallest prime divisor as 100(99! - 1), but by Wilson's Theorem,







Therefore 101 is the smallest prime divisor of 99! - 1

dcc:
show that:

Ahmad:

--- Quote from: dcc on March 28, 2008, 03:12:58 pm ---show that:




--- End quote ---

Use the above result to show that,


Hence, show that,

Mao:

--- Quote from: dcc on March 28, 2008, 03:12:58 pm ---show that:


--- End quote ---

this sucks:

let k be a natural number

by the double angle formular for sin(x):














if we let k=c=n





since the two are algebraically equal:





QED

*and VICTORY*

but i dont like that last step applying the limits to both sides........ :(

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