Is there an efficient way to work out how many factors a large number has?
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?
Helen made the conjecture that "every multiple of six has more
factors than the two numbers either side of it". Is this conjecture
When asked how old she was, the teacher replied:
Or you can reverse and subtract, and
again you have a perfect square.