What fractions can you find between the square roots of 56 and 58?

Find the polynomial p(x) with integer coefficients such that one solution of the equation p(x)=0 is $1+\sqrt 2+\sqrt 3$.

The squares of any 8 consecutive numbers can be arranged into two sets of four numbers with the same sum. True of false?

This problem is taken from the UKMT Mathematical Challenges.View the archive of all weekly problems grouped by curriculum topic