Define a "primitive harmonic triplet" as any ordered triplet (x,y,z), where x,y,z∈Z+ and gcd(x,y,z)=1, such that
x1+y1=z1.
Are there infinitely many primitive harmonic triplets?
- If the answer is no, enter the number of ordered pairs (x,y) such that (x,y,6) is a primitive harmonic triplet.
- If the answer is yes, enter the number of ordered pairs (x,y) such that (x, y, 25×34×53×72×11) is a primitive harmonic triplet.
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