Are Pythagorean Triplets Infinite?
<p><strong><span style="color:#8e44ad;">Are Pythagorean Triplets Infinite?</span></strong></p>
<p>Yes. For two reasons.</p>
<p><strong><span style="color:#e74c3c;">Reason 1</span></strong></p>
<p>You can create an infinite number of Pythagorean triplets simply by multiplying each side of a known Pythagorean triplet (like $3$-$4$-$5$) by any positive multiple. See below:</p>
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<p><strong><span style="color:#e74c3c;">Reason 2</span></strong></p>
<p>You can simply use the formulas below to find the three sides of an infinite number of Pythagorean triplets. Select two positive integers, $m$ and $n$, where $n > m$, and then use these three formulas:</p>
<p style="text-align: center;"><span style="color:#27ae60;">Side 1</span></p>
<p style="text-align: center;">$$2mn$$</p>
<p style="text-align: center;"><span style="color:#27ae60;">Side 2</span></p>
<p style="text-align: center;">$$n^2 - m^2$$</p>
<p style="text-align: center;"><span style="color:#27ae60;">Hypotenuse</span></p>
<p style="text-align: center;">$$m^2 +n^2$$</p>
<p>For example, if we select $m = 4$ and $n = 7$, we find the Pythagorean triplet $33$-$56$-$65$.</p>