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HEXA Challenge Section Editor: Eric Choate

With every issue of Virginia Mathematics Teacher that is released, we include six HEXA Challenge questions. The answers to this issue will be featured in the 48(2) version of the journal. See the section “ Solutions to 47(2) HEXA Challenge Problems ” towards the back of the journal for solutions to the problems featured in our previous issue.

Problems created by: Eric P. Choate, Charlene J. Galvez, Adam Downs

Challenge 1:

If is a positive integer, prove that

is also an integer.

Challenge 2:

Let

be an even polynomial that passes through the points

,

and

.

What conditions must , and satisfy in order for the degree of

to be less than 4.

Challenge 3:

For what slopes does the line

intersect the parabola

?

Virginia Mathematics Teacher vol. 48, no. 1

56