### Consecutive Numbers

An investigation involving adding and subtracting sets of consecutive numbers. Lots to find out, lots to explore.

### 14 Divisors

What is the smallest number with exactly 14 divisors?

### Summing Consecutive Numbers

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?

# Tenth Power

##### Stage: 3 Short Challenge Level:

$3$ is odd and the product of two odd numbers is always odd therefore (2) is true, which means that $3^{10}$ is certainly not even, so (1) is false.

$3^{10} = \left( 3^5 \right)^2$, so it is also a perfect square, meaning (3) is also true.

This problem is taken from the UKMT Mathematical Challenges.
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