This One Equation, $10² + 11² + 12² = 13² + 14²$, Takes Pythagoras To A Whole New Level

One of the first theorems anyone learns in mathematics is the Pythagorean Theorem: if you have a right triangle, then the square of the longest side (the hypotenuse) will always equal the sums of the squares of the other two sides. 

The first integer combination that this works for is a triangle with sides $3, 4$, and $5$: $3² + 4² = 5²$. 

There are other combinations of numbers that this works for, too, including:

$5, 12$, and $13$,

$6, 8$, and $10$,

$7, 24$ and $25$

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