An investigation involving adding and subtracting sets of consecutive numbers. Lots to find out, lots to explore.
What is the smallest number with exactly 14 divisors?
Many numbers can be expressed as the sum of two or more consecutive integers. For example, 15=7+8 and 10=1+2+3+4. Can you say which numbers can be expressed in this way?
This is the only solution of the equation for which x and y are whole numbers. Another way of looking at this is to say that 26 is the only whole number "sandwiched" between a perfect square and a perfect cube. This was proved by the French mathematician, Pierre de Fermat, in the 17th Century.
This problem is taken from the UKMT Mathematical Challenges.