If x + (1/x) = (√3 + 1)/2, then what is the value of x4 + (1/x4)?

If x and y are natural numbers such that x + y = 2017, then what is the value of (– 1)x+ (– 1)y?

If α and β are the roots of the equation x2+ x – 1 = 0, then what is the equation whose roots are α5 and β5?

p3 + q3 + r3 – 3pqr = 4. If a = q + r, b = r + p and c = p + q, then what is the value of a3 + b3 + c3 – 3abc?

What is the value of √121 + √12321 + √1234321 + √123454321?

How many natural numbers are there between √261 and √45109?

N is the smallest three digit prime number. When N is divided by 13, then what will be the remainder?

x, y and z are prime numbers and x + y + z = 38. What is the maximum value of x?