Problem 31

A two-digit integer n has the property that the sum of n and its digits is equal to 63. Find n.

Problem 30

Compare 65²³ and 255¹⁷.

Problem 29

Factorise P(x) =  2x⁷ + 5x⁴ + 3.

Problem 28

Let ABC an isoceles triangle with AB = AC = x, BC = y. Let denote M the midpoint of AB. Find the length of CM.

Problem 27

A triangle has side lengths 15, 13 and 4 cm. Find the length of the longest altitude.

Problem 26

Prove that every composite number has a proper factor less than or equal to its square root.

Problem 25

Show that 43ⁿ + 83 x 92^3n-1 is divisible by 7 for all positive integers n.