1.

Using the binomial theorem show that 1^(99) + 2^(99) +3^(99) + 4^(99) + 5^(99) is divisible by 3 and 5 so that it is actually divisible by 15.

Answer»

SOLUTION :From EQN. (1) above, it is clear that each term within the 1st brackets is divisible by 3 and the TERMS in the 2nd bracket is divisible by 99 and HENCE divisible by 3.
therefore Each term in eqn.(1) is divisible by 3 and 5 , it is divisible by `3xx5` = 15.


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