What fractions can you find between the square roots of 65 and 67?
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?
Derek (no school given) offered the
following insights into this problem: - and nicely explained too -
thank you Derek.
Editor's comment: at this point it may be
worth mentioniing that the sum of the binomial coefficients are
powers of 2. Why?
Chen of the Chinese High School took a
slightly different approach (similar to the one offered by Andrei
of Tudor Vianu National College):