If `(4+sqrt(15))^n=I+f,w h r en` is an odd natural number, `I` is an integer and `0

Find the sum of first 15 odd natural numbers.

If (2+sqrt(3))^n=I+f, whare I and n are positive integers and 0

If (9 + 4 sqrt(5))^(n) = I + f ,n and l being positive integers and f is a proper fraction , show that (I-1 ) f + f^(2) is an even integer.

If x , y >0,(log)_y x+(log)_x y=(10)/3 a n d x y=144 , t h e n(x+y)/2=sqrt("N")" w h e r e N" is a natural number, find the value of Ndot

Let N=(log_(3)135)/(log_(15)3)-(log_(3)5)/(log_(405)3). Then N is a natural number (b) a prime number an even integer (d) an odd integer

If n is a positive integer,then (sqrt(3)+1)^(2n)-(sqrt(3)-1)^(2n) is (1) an irrational number (2) an odd positive integer (3) an even positive integer (4) a a rational number other than positive integers

If following form the above example that (-1) an odd natural number quad =-1 and (-1) An even natural number =1 i.e.(-1)^(n)={1 if n is an even natural number and -1 if n is odd natural number