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
A spreadsheet was a really useful tool for looking for patterns
by quickly calculating powers of each of the numbers and then
looking for patterns, but not for explaining why. Why is the power
always of the form 2k+1 of 4k+2 except for 5 n + 5
Here are some combinations (n and k are integers):