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Statement 1: If p is a prime number (p!=...

Statement 1: If `p` is a prime number `(p!=2),` then `[(2+sqrt(5))^p]-2^(p+1)` is always divisible by `p(w h e r e[dot]` denotes the greatest integer function). Statement 2: if `n` prime, then `^n C_1,^n C_2,^n C_2 ,^n C_(n-1)` must be divisible by `ndot`

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Prove that if p is a prime number greater than 2, then the difference [(2+sqrt(5))^(p)]-2^(p+1) is divisible by p,where [.] denotes greatest integer.

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Statement-1: the highest power of 3 in .^(50)C_(10) is 4. Statement-2: If p is any prime number, then power of p in n! is equal to [n/p]+[n/p^(2)]+[n/p^(3)] + . . ., where [*] denotes the greatest integer function.