If in a positive integer such that If a number a=p+f whre p is an integer and `0ltflt1`. Here p is called the integral part of a and f its fractional part. Let `n in N` and `(sqrt(3)+1)^(2n)=p+f`, where p is the integral part and `0ltflt1`. On the basis of bove informationi answer teh following question:
`f^2+(p-1)f+4^n=`
(A) p (B) `-p` (C) 2p (D) `-2p`

If in a positive integer such that If a number a=p+f whre p is an integer and 0ltflt1 . Here p is called the integral part of a and f its fractional part. Let n in N and (sqrt(3)+1)^(2n)=p+f , where p is the integral part and 0ltflt1 . On the basis of bove informationi answer teh following question: The integral part p of (sqrt(3)+1)^(2n) is (A) an even number for al n epsilon N (B) an odd number for all nepsilon N (C) anodd or even number according as n is odd or even (D) an even or odd nuber according as n is odd or even

If n and p are positive integers such that 8(2^(p))=4^(n) , what is n in terms of p?

If (8 + 3sqrt(7))^(n) = P + F , where P is an integer and F is a proper fraction , then

If (3sqrt(3)+5)^n=p+f. where p is an integer and f is a proper fraction. then find the value of (3sqrt3-5)^n,nin,N, is

If p^(2)-p+1=0 , then the value of p^(3n) can be

If (3sqrt3 + 5)^7 = P + F where P is an integer and F is a proper fraction, then F(P + F) =

If f(x) = px +q, where p and q are integers f (-1) = 1 and f (2) = 13, then p and q are

A be the set of two positive integers and f: A -> Z^+ (set of positive integer) defined as f(n)= p where p is the largest prime factor of n. If the range of f is {3} , find A.

If p is a fixed positive integer, prove by induction that p^(n +1) + (p + 1)^(2n - 1) is divisible by P^2+ p +1 for all n in N .

Theorem 1.3 : Let p be a prime number. If p divides a^2 , then p divides a, where a is a positive integer.