I'm hoping on making the United States of America Math Olympiad for Highschool Students this year and i need some help on these questions. Future help will be appreciated. Please make the solutions easy to understand and to follow, please. Hints would be the best.(adsbygoogle = window.adsbygoogle || []).push({});

how many primes, p, make 13p^4-888 a positive prime?

Thoughts: I have no idea of where to begin. A hint would be nice on this one.

Let a1, a2, a3........ be the numbers which can be written as a sum of one of more different powers of 4 with a1<a2<a3..... e.g. 4^0=a1, 4^1=a2, 4^0+4^1=a3. find a70

Thoughts: It sounds to me that its going by the binomial theorem for example, 210. 3!/(1!)(2!)= 3 ways of having only one term. 3!/(2!)(1!)= 3 ways of having two terms. 1 way of having all. I hope im on the right track. So do i set up the sigma:

_x_

\ x!/{(x-n)!n!} = 70, or around there.

/__

n=1

Im so lost!

The sides of triangle ABC have length AB=7, BC=8, and AC=9. The distance between the incenter and the orthocenter of triangle ABC is

Thoughts: So the incenter is where the medians intersect?, and the orthocenter is?

Thanks in advance, -Matt

**Physics Forums | Science Articles, Homework Help, Discussion**

Dismiss Notice

Join Physics Forums Today!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

# Competition that i need to pass

**Physics Forums | Science Articles, Homework Help, Discussion**