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A103249
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Numbers y, without duplication, in Pythagorean triples x,y,z where x,y,z are relatively prime composite numbers and x is a perfect square.
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1
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3, 12, 17, 27, 48, 63, 68, 75, 77, 99, 108, 147, 153, 192, 243, 252, 272, 300, 301, 308, 323, 363, 396, 399, 425, 432, 507, 561, 567, 577, 588, 612, 621, 675, 693, 768, 833, 867, 891, 943, 972, 1008, 1023, 1083, 1088, 1200, 1204, 1232, 1292, 1323, 1377, 1377
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OFFSET
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1,1
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COMMENTS
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There exists no case in which x and y are both squares.
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LINKS
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Chenglong Zou, Peter Otzen, Cino Hilliard, Pythagorean triplets, digest of 6 messages in mathfun Yahoo group, Mar 19, 2005.
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EXAMPLE
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y=3, x=4, 4^2 + 3^2 = 5^2. 3 is the 1st entry in the list.
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PROG
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(PARI) pythtrisq(n) = { local(a, b, c=0, k, x, y, z, vy, j); w = vector(n*n+1); for(a=1, n, for(b=1, n, x=2*a*b; y=b^2-a^2; z=b^2+a^2; if(y > 0 & issquare(x), c++; w[c]=y; print(x", "y", "z) ) ) ); vy=vector(c); w=vecsort(w); for(j=1, n*n, if(w[j]>0, k++; vy[k]=w[j]; ) ); for(j=1, 200, print1(vy[j]", ") ) }
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CROSSREFS
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KEYWORD
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easy,nonn
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AUTHOR
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STATUS
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approved
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