## Ukc field trials

Q: Find f(g(x)) and g(f(x)) and determine whether the pair of functions f and g are inverses of each ot...

Jan 12, 2009 · Find three consecutive integers such that the sum of the first and second is three more than three times the? third. I can't figure out what numbers i'm suppose to use to solve this.

Jul 11, 2007 · A 2. Find in nitely many triples (a;b;c) of positive integers such that a, b, care in arithmetic progression and such that ab+ 1, bc+ 1, and ca+ 1 are perfect squares. AMM, Problem 10622, M. N. Deshpande A 3. Let aand bbe positive integers such that ab+ 1 divides a2 + b2. Show that a2 + b2 ab+ 1 is the square of an integer. IMO 1988/6 A 4.

Find three consecutive odd integers such that the sum of the largest and twice the smallest is 25. If x represents the smallest integer, then which equation could be used to solve the problem?

Determine all pairs m,n of nonzero integers such that the only admissible set containing both m and n is the set of all integers. N2. Find all triples (x,y,z) of positive integers such that x ≤ y ≤ z and x3(y3 +z3) = 2012(xyz +2). N3. Determine all integers m ≥ 2 such that every n with m 3 ≤ n ≤ m 2 divides the binomial coeﬃcient n ...

Find three consecutive odd integers such that the sum of 7 times the smallest and twice the larQest is —91. -57, -55 58, 60 0 77, 79 54, 56 Solving Problems Involving Consecutive Integers ©2006 Marcy Mathworks 48, 50, 52 the largest and 5 times the smallest is —244. -11,- 7 Find two consecutive even integers such that the sum of the larger ...