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Topic: Pythagorean triples (a,b,c) & (a,nb,d) (was "A few sheets of paper")
Replies: 3   Last Post: Dec 28, 2004 6:55 PM

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anonymous

Posts: 253
Registered: 12/6/04
Re: Pythagorean triples (a,b,c) & (a,nb,d) (was "A few sheets of paper")
Posted: Dec 28, 2004 6:55 PM
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>> Are there any values a,b,c,d,n which give a^2+b^2=c^2 and
>> a^2+(nb)^2=d^2 for n<7? I have tried without success
>> either to find such a solution or to prove none exists,
>> even for the apparently simple case n=2.

none for n<7, however for n>=7 there are solutions

n = 7, a,b = 12,5
n = 10, a,b = 35,12
n = 11, a,b = 21,20
n = 12, a,b = 112,15
n = 14, a,b = 112,15
n = 17, a,b = 528,455

see <a href="http://maths.paisley.ac.uk/allanm/ECRNT/dickdood/conc.htm">http://maths.paisley.ac.uk/allanm/ECRNT/dickdood/conc.htm</a> about this for
more solutions. This is related to the Concordant number problem.

Randall




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