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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




Re: Pythagorean triples (a,b,c) & (a,nb,d) (was "A few sheets of paper")
Posted:
Dec 28, 2004 6:55 PM


>> 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



