Can two pythagoras triplet have a common number If I have a pythagoras triplet $(a,b,c)$ such that $$a^2+b^2=c^2$$ then is there another triplet $(a,d,e)$ possible such that $$a^2+d^2=e^2, \; b\neq d$$--prophetes.ai

Can two pythagoras triplet have a common number If I have a pythagoras triplet $(a,b,c)$ such that $$a^2+b^2=c^2$$ then is there another triplet $(a,d,e)$ possible such that $$a^2+d^2=e^2, \; b\neq d$$

Let's rewrite the equation as

$$a^2=(c+b)(c-b)$$

Different factorizations of $a^2$ lead to different triples. For example, if $a=15$, try $c+b=225$ and $c+b=25$.