# Difference between revisions of "Pre-Olympiad Level Tournament By Mathtime"

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− | Prove that there is no positive integers <math>k</math> such that <math>\frac{ | + | Prove that there is no positive integers <math>k</math> such that <math>\frac{(x^2+y^2+xz)+x^m*y^z}{x^2-y^2}=3+kx+ky\ \forall x,y \in \mathbb{N}</math>, and this equation must satify for all <math>x</math> and <math>y</math>, and <math>m</math> and <math>z</math> are positive integers. |

## Latest revision as of 16:06, 7 January 2012

# Problem 1

Suppose we have a sequence, with the first term equal to , with , an a second term of and each term after that, equal to , which is the 'th Fibonacci number. Assume that is always an integer in this problem, and that must always be an integer in this problem.

Find (with proof) all integers , such that this sequence has the integer in it.

# Problem 2

In a cyclic quadrilateral with sides prove that:

# Problem 3

Prove that there is no positive integers such that , and this equation must satify for all and , and and are positive integers.