Can you spot the pattern here?

Another simple way to generate this pattern is to take any odd number as $a$ , then find $a^2$ and split it as evenly as possible into whole numbers $b$ and $c$ . For example:

• $a = 13$ : $\qquad a^2 = 169 = 84 + 85 \qquad \quad$ generates $(13, 84, 85)$
• $a = 19$ : $\qquad a^2 = 361 = 180 + 181 \qquad$ generates $(19, 180, 181)$
• $a = 27$ : $\qquad a^2 = 729 = 364 + 365 \qquad$ generates $(27, 364, 365)$

etc. As the last two numbers are consecutive the triples will always be primitive.

The general formula for these triples is $(2n + 1, 2n^2 + 2n, 2n^2 + 2n + 1)$ ; simple algebra proves it generates Pythagorean triples for all $n \in \mathbb{N}$ .

For the answer to the question, we need $n=7^7$ ; the sum will be $4n^2 + 6n + 2 = 4(7^{14}) + 6(7^7) + 2 = \boxed{2712897232656}$

See my most recent post about Pythagorean Triples for the solution and the rule to the pattern. We have $a = 1647087, b = 1356447792784, c = 1356447792785$ .

What... HOW IS THIS ONLY LEVEL 2?? Can somenoe pls make it Level 3?