Problem 4 · 2016 Math Kangaroo
Medium
Algebra & Patterns
difference-of-squares
How many whole numbers are bigger than \(2015 \times 2017\) but smaller than \(2016 \times 2016\)?
Show answer
Answer: A — 0
Show hints
Hint 1 of 2
The two products straddle a perfect square; look for a difference of squares.
Still stuck? Show hint 2 →
Hint 2 of 2
Rewrite \(2015 \times 2017\) as \((2016-1)(2016+1)\).
Show solution
Approach: difference of squares
- Rewrite \(2015 \times 2017 = (2016-1)(2016+1) = 2016^2 - 1\).
- So the two bounds are \(2016^2 - 1\) and \(2016^2\), which are consecutive integers.
- Nothing lies strictly between two consecutive integers, so the count is 0 (A).
Mark:
· log in to save