Unanswered Questions

A triangle ABC has \(\widehat{A}=120^o\) and the bisector AD \(\left(D\in BC\right)\). If AB = 40 cm, AD = 30 cm then AC = ...

The operation @ on two numbers produces a number equal to their sum minus 2. The value of  (1 @ 2 @ 3 @ ... @ 2017)

Bill buys wigits for $3, gigits for $8 and pigits for $11. If Bill bought exactly 100 aliens for $400, and he purchased as few gigits as possible, what is the ordered triple (wigits, gigits, pigits) that represents his purchase? 

What are the coordinates of the first-quadrant point that lies on the graph of 7x + 13y = 99 and has coordinates that are both integers? Express your answer as an ordered pair (x, y). 

What is the smallest positive integer value of n such that 2ⁿ + 5ⁿ + 7ⁿ  is a multiple of 17?

Using exponents when prime factors are used more than once, what is the prime factorization of 504?

Many numbers can be made by adding two or more consecutive terms of the arithmetic sequence 2, 5, 8, 11, … . Two such examples are 7 = 2 + 5 and 24 = 5 + 8 + 11. What is the smallest number that can be made in at least two different ways by adding consecutive terms of this sequence? 

Prove that for any integer x, y then

A = (x + y) (x + 2y) (x + 3y) (x + 4y) + y⁴ is a perfect square.

Let ABCD be the square with the side length 56 cm. If E and F lie on CD, BC respectively that CF = 14 cm, and \(\widehat{EAF}=45^o\) then CE = ...

Given \(f\left(x\right)=\dfrac{2x^2+3x+3}{2x-1}\). If a and f (a) are both integers, we say that f (a) is an element of the set A. What is the sum of all elements of the set A?