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?
The standard Fibonacci sequence 1, 1, 2, 3, 5, 8, 13, ? begins with two 1s and each later number in the sequence is the sum of the previous two numbers. Other Fibonacci-like sequences can be constructed by starting with any two numbers a and b (not necessarily 1 and 1) and using the same rule for creating the other numbers in the sequence. What is the first term of the Fibonacci-like sequence
whose second term is 4 and whose fifth term is 22?
This problem is taken from the UKMT Mathematical Challenges.