Pre-Olympiad Level Tournament By Mathtime
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.
In a cyclic quadrilateral with sides prove that:
Prove that there is no positive integers such that , and this equation must satify for all and , and and are positive integers.