Question: using binomial theorem prove that 2^3n-7 n-1 is divisible by 49?
Answer: Using binomial theorem, prove that 23n-7n-1 is divisible by 49 , where n∈N. Now, C(n,0)7n+C(n,1)7n-1+... +C(n,n-2)72 is clearly divisible by 49. ... So, clearly 23n-7n-1 is divisible by 49.