Henry Ernest Dudeney/Puzzles and Curious Problems/126 - Making Squares/Solution

Puzzles and Curious Problems by Henry Ernest Dudeney: $126$

Making Squares

Find three whole numbers in arithmetic progression,

the sum of every two of which shall be a square.

Solution

We have the set:

$\set {482, 3362, 6242}$

which have a common difference of $2880$.

We see that:

\(\ds 482 + 3362\)

\(=\)

\(\ds 3844\)

\(\ds 62^2\)

\(\ds 482 + 6242\)

\(=\)

\(\ds 6724\)

\(\ds 82^2\)

\(\ds 3362 + 6242\)

\(=\)

\(\ds 9604\)

\(\ds 98^2\)

Proof

This theorem requires a proof. In particular: There may be a way to arrive at this by using the Odd Number Theorem -- it's served us well enough in the past. You can help $\mathsf{Pr} \infty \mathsf{fWiki}$ by crafting such a proof. To discuss this page in more detail, feel free to use the talk page. When this work has been completed, you may remove this instance of {{ProofWanted}} from the code. If you would welcome a second opinion as to whether your work is correct, add a call to {{Proofread}} the page.

Sources

• 1932: Henry Ernest Dudeney: Puzzles and Curious Problems ... (previous) ... (next): Solutions: $126$. -- Making Squares
• 1968: Henry Ernest Dudeney: 536 Puzzles & Curious Problems ... (previous) ... (next): Answers: $199$. Making Squares