Squares and Pairs
Algebra
Level
2
Take a pair of numbers that are an even distance apart, then multiply them together.
\[\begin{align} 2\times 4&=8 \\ 20\times 36&=720 \\ 519\times 93&=48267 \end{align} \]
With these three examples, we see a peculiar pattern emerge.
\[\begin{align} 8+1^2 & = 3^2 \\ 720 + 8^2 & = 28^2\\ 48267 + 213^2 & = 306^2 \end{align} \]
Each of these products are some square number less than another square number!
Is this the case for every pair of numbers with even distance?
by
Eric Schneider