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(But )Tj
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(this )Tj
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(illusion. )Tj
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(an )Tj
0.0141 Tc 9 0 0 9 37.04 518.23 Tm
(For )Tj
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0 Tc 1.6773 0 0 7.3801 53.83 518.23 Tm
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(i\(j\) )Tj
/T1_0 1 Tf
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(0 )Tj
0.0174 Tc 0.919 0 Td
(for )Tj
/T1_2 1 Tf
0 Tc 9.6 0 0 9.6 185.72 518.23 Tm
(j )Tj
/T1_0 1 Tf
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(> )Tj
/T1_2 1 Tf
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(jo. )Tj
/T1_0 1 Tf
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(Then )Tj
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(Condition )Tj
0 Tc 9 0 0 9 291.68 518.23 Tm
(3 )Tj
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(only )Tj
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(needs )Tj
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(to )Tj
9.335 0 0 9 360.55 518.23 Tm
(be )Tj
/T1_2 1 Tf
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(jo\) )Tj
/T1_0 1 Tf
0.05 Tc 9.2824 0 0 9 104.13 506.71 Tm
(and )Tj
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(Condition )Tj
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(4 )Tj
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(only )Tj
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(for )Tj
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(jo. )Tj
/T1_0 1 Tf
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(\(This )Tj
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(further )Tj
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(the )Tj
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(direct )Tj
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(sum )Tj
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(in )Tj
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(Condition )Tj
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(5 )Tj
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(is )Tj
0 Tc 1.078 0 Td
(a )Tj
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(finite )Tj
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(one.\) )Tj
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(Condition )Tj
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(there )Tj
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(the )Tj
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(matter )Tj
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(of )Tj
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(det;erJmlJllInLg )Tj
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(if )Tj
0.05 Tc 9.0189 0 0 9 325.24 484.03 Tm
(two )Tj
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(rooted )Tj
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(trees )Tj
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(are )Tj
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('OATYlf" )Tj
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(... )Tj
5.4769 0 0 4.5001 89.58 473.59 Tm
(-n,h )Tj
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(to )Tj
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(have )Tj
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(been )Tj
/C0_0 1 Tf
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<002C005500220022007E00220074004A00270027002D002700550027005500560020>Tj
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(\225\225 )Tj
/T1_3 1 Tf
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(V.L )Tj
/T1_0 1 Tf
0 Tc 4.2 0 0 4.2 135.9 460.99 Tm
(y )Tj
0.0423 Tc 9 0 0 9 143.56 460.99 Tm
(discovered )Tj
0.05 Tc 9.2072 0 0 9 189.88 460.99 Tm
(many )Tj
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(times )Tj
0.0218 Tc 9 0 0 9 241.83 460.99 Tm
(over; )Tj
0.0456 Tc 8.629 1.28 Td
(which )Tj
0.0311 Tc 3.047 0 Td
(seems )Tj
/T1_3 1 Tf
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([2J )Tj
/T1_0 1 Tf
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(for )Tj
0.05 Tc 9.7155 0 0 9 313.1 461.17 Tm
(an )Tj
-0.0216 Tc 9 0 0 9 327.18 461.17 Tm
(Int,ere:StlIlg )Tj
0.0311 Tc -33.854 -1.3 Td
(history. )Tj
0.0307 Tc 1.637 -1.26 Td
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(that )Tj
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(ln )Tj
0.0464 Tc 9 0 0 9 96.14 438.13 Tm
(Section )Tj
-0.0206 Tc 4.457 0 Td
(we )Tj
0.0388 Tc 1.512 0 Td
(defined )Tj
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(n )Tj
/T1_0 1 Tf
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(to )Tj
0.0466 Tc 9 0 0 9 201.25 438.13 Tm
(be )Tj
0.05 Tc 9.5625 0 0 9 213.28 438.13 Tm
(the )Tj
9.4453 0 0 9 228.7 438.13 Tm
(lcm )Tj
0.0274 Tc 9 0 0 9 246.33 438.13 Tm
(of )Tj
0.05 Tc 9.5625 0 0 9 256.84 438.13 Tm
(the )Tj
/T1_1 1 Tf
0 Tc 8.8 0 0 8.8 287.82 438.13 Tm
(S )Tj
/T1_0 1 Tf
0.05 Tc 9.1816 0 0 9 296.91 438.13 Tm
(of )Tj
9.5625 0 0 9 22.66 426.61 Tm
(the )Tj
/T1_2 1 Tf
0 Tc 8.8 0 0 8.8 136.03 426.61 Tm
(n )Tj
/T1_0 1 Tf
-0.0099 Tc 9 0 0 9 144.83 426.61 Tm
(is )Tj
0.05 Tc 9.8357 0 0 9 154.6 426.61 Tm
(the )Tj
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(order )Tj
0.0274 Tc 9 0 0 9 195.57 426.61 Tm
(of )Tj
0.05 Tc 9.4259 0 0 9 206.08 426.61 Tm
(the )Tj
9.5145 0 0 9 280.6 426.61 Tm
(And )Tj
/T1_2 1 Tf
0 Tc 8.8 0 0 8.8 301.63 426.61 Tm
(n )Tj
/T1_0 1 Tf
0.0239 Tc 9 0 0 9 37.28 414.91 Tm
(Since )Tj
/T1_2 1 Tf
-0.035 Tc 9.6059 0 0 10.3 60.85 414.91 Tm
(1r\(i\) )Tj
/T1_1 1 Tf
0 Tc 8.8 0 0 8.8 139.5 414.91 Tm
(S )Tj
/T1_3 1 Tf
9.9 0 0 9.9 148.95 414.91 Tm
(I )Tj
0.05 Tc 11.565 0 0 9.9 153.52 414.91 Tm
(jli}\), )Tj
/T1_0 1 Tf
9.0095 0 0 9 178.65 414.91 Tm
(Condition )Tj
0 Tc 9.4 0 0 9.4 221.82 414.91 Tm
(6 )Tj
0.05 Tc 9.298 0 0 9 229.13 414.91 Tm
(need )Tj
0.0478 Tc 9 0 0 9 251.19 414.91 Tm
(only )Tj
0.05 Tc 10.0672 0 0 9 271.81 414.91 Tm
(be )Tj
9.0205 0 0 9 285.21 414.91 Tm
(checked )Tj
0.0074 Tc 9 0 0 9 320.48 414.91 Tm
(for )Tj
0.05 Tc 9.5625 0 0 9 22.84 403.75 Tm
(the )Tj
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(same )Tj
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(formula )Tj
9.2091 0 0 9 98.01 403.75 Tm
(can )Tj
9.335 0 0 9 115.21 403.75 Tm
(be )Tj
9.0845 0 0 9 128.16 403.75 Tm
(used )Tj
9.6041 0 0 9 149.92 403.75 Tm
(to )Tj
0.0433 Tc 9 0 0 9 161.65 403.75 Tm
(prove )Tj
0.05 Tc 9.4259 0 0 9 187.18 403.75 Tm
(the )Tj
10.5629 0 0 9.1 22.98 387.01 Tm
(Lemma )Tj
0 Tc 9.1 0 0 9.1 61.09 387.01 Tm
(6 )Tj
/T1_2 1 Tf
0.05 Tc 9.682 0 0 8.9 71.56 387.01 Tm
(Let )Tj
8.9432 0 0 8.9 23.76 375.49 Tm
(Condition )Tj
-0.035 Tc 8.4423 0 0 8.9 67.35 375.49 Tm
(6, )Tj
/T1_0 1 Tf
6.2928 0 0 12.3 100.38 386.65 Tm
(cF )Tj
/T1_2 1 Tf
0 Tc 8.7 0 0 8.7 110.09 386.65 Tm
(p )Tj
-0.035 Tc 8.3188 0 0 8.7 118.92 386.65 Tm
(be )Tj
0 Tc 8.7 0 0 8.7 130.98 386.65 Tm
(a )Tj
0.05 Tc 9.0753 0 0 8.7 138.91 386.65 Tm
(prime, )Tj
0 Tc 8.7 0 0 8.7 169.36 386.65 Tm
(k )Tj
/T1_0 1 Tf
0.969 0 Td
(E )Tj
12.1 0 0 12.1 107.76 375.67 Tm
(= )Tj
/C0_0 1 Tf
3.8001 0 0 8.1 117.54 375.67 Tm
<0036002700280070007E002D006C005800290020>Tj
/T1_2 1 Tf
0.0033 Tc 8.9 0 0 8.9 172.02 375.67 Tm
(all )Tj
0 Tc 1.474 0 Td
(x )Tj
0.0424 Tc 1.542 1.254 Td
(with )Tj
/T1_3 1 Tf
0.0327 Tc 8.3 0 0 8.3 201.62 374.23 Tm
(p" )Tj
0 Tc 12.7 0 0 12.7 229.83 386.83 Tm
(f )Tj
/T1_2 1 Tf
0.05 Tc 10.1057 0 0 8.9 235.75 386.83 Tm
(n. )Tj
0.0268 Tc 8.9 0 0 8.9 249.91 386.83 Tm
(For )Tj
0.05 Tc 8.905 0 0 8.9 267.74 386.83 Tm
(the )Tj
9.4472 0 0 8.9 283.46 386.83 Tm
(function )Tj
/T1_3 1 Tf
-0.035 Tc 6.0346 0 0 9.3 321.96 386.83 Tm
(6' )Tj
/T1_2 1 Tf
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(defined )Tj
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(by )Tj
/T1_0 1 Tf
0 Tc 12.5 0 0 12.5 366.18 374.95 Tm
(o )Tj
0.05 Tc 9.0105 0 0 9 37.71 358.75 Tm
(Conditions )Tj
0 Tc 8.9 0 0 8.9 85.77 358.75 Tm
(7 )Tj
0.05 Tc 9.3999 0 0 9 94.4 358.75 Tm
(and )Tj
0 Tc 8.9 0 0 8.9 112.88 358.75 Tm
(8 )Tj
0.05 Tc 9.1537 0 0 9 120.95 358.75 Tm
(range )Tj
0.0415 Tc 9 0 0 9 147.15 358.75 Tm
(over )Tj
0.027 Tc 2.36 0 Td
(all )Tj
/T1_1 1 Tf
0 Tc 7.6 0 0 7.6 210.45 358.75 Tm
(p )Tj
/T1_3 1 Tf
12.7 0 0 12.7 218.13 358.75 Tm
(f )Tj
/T1_0 1 Tf
0.05 Tc 9.5174 0 0 9 235.16 358.75 Tm
(and )Tj
0.037 Tc 9 0 0 9 254.07 358.75 Tm
(all )Tj
/T1_2 1 Tf
0 Tc 9.9 0 0 9.9 267.36 358.75 Tm
(t )Tj
/T1_0 1 Tf
-0.0215 Tc 8.9 0 0 8.9 284.8 358.75 Tm
(N. )Tj
-0.035 Tc 8.9557 0 0 9 342.71 358.75 Tm
(we )Tj
0.047 Tc 9 0 0 9 356.85 358.75 Tm
(can )Tj
0.05 Tc 9.0528 0 0 9 23.03 347.23 Tm
(restrict )Tj
0.0458 Tc 9 0 0 9 56.43 347.23 Tm
(ourselves )Tj
0.05 Tc 9.3858 0 0 9 98.26 347.23 Tm
(to )Tj
/T1_2 1 Tf
0 Tc 10 0 0 10 110.58 347.23 Tm
(t )Tj
-0.035 Tc 9.465 0 0 10 130.03 347.23 Tm
(to. )Tj
/T1_0 1 Tf
0.05 Tc 9.4154 0 0 9 147.4 347.23 Tm
(And )Tj
9.5625 0 0 9 169.18 347.23 Tm
(the )Tj
0.0069 Tc 9 0 0 9 186.2 347.23 Tm
(following )Tj
0.05 Tc 9.3765 0 0 9 226.6 347.23 Tm
(theorem )Tj
0.0363 Tc 9 0 0 9 264.47 347.23 Tm
(shows )Tj
0.05 Tc 10.1785 0 0 9 293.38 347.23 Tm
(that )Tj
-0.0006 Tc 9 0 0 9 315.35 347.23 Tm
(we )Tj
0.05 Tc 9.1209 0 0 9 330.29 347.23 Tm
(need )Tj
0.0411 Tc 9 0 0 9 353.43 347.23 Tm
(only )Tj
0.0278 Tc -36.68 -1.26 Td
(check )Tj
0.05 Tc 9.1302 0 0 9 48.22 335.89 Tm
(those )Tj
0 Tc 6 0 0 6 73.18 335.89 Tm
(5 )Tj
0.05 Tc 9.1449 0 0 9 80.99 335.89 Tm
(which )Tj
0.0464 Tc 9 0 0 9 108.64 335.89 Tm
(divide )Tj
/T1_3 1 Tf
0.05 Tc 9.1502 0 0 7.9001 136.26 335.89 Tm
(m. )Tj
/T1_0 1 Tf
10.644 0 0 9.1 23.31 318.97 Tm
(Theorem )Tj
0 Tc 9.1 0 0 9.1 69.17 318.97 Tm
(5 )Tj
/T1_2 1 Tf
0.0497 Tc 8.9 0 0 8.9 79.73 318.97 Tm
(Suppose )Tj
0.05 Tc 9.1483 0 0 8.9 116.64 318.97 Tm
(Condition )Tj
/T1_0 1 Tf
0 Tc 9.1 0 0 9.1 161.36 318.97 Tm
(7 )Tj
/T1_2 1 Tf
0.0217 Tc 8.9 0 0 8.9 168.97 318.97 Tm
(holds, )Tj
-0.035 Tc 8.0975 0 0 8.9 196.33 318.97 Tm
(aenmt'f,uJ )Tj
-0.0199 Tc 10.1 0 0 10.1 230.84 318.97 Tm
(Ps\(t\). )Tj
0.05 Tc 9.3524 0 0 8.9 258.47 318.97 Tm
(Then )Tj
-0.0202 Tc 10.1 0 0 10.1 282.5 318.97 Tm
(Ps\(t\) )Tj
/T1_0 1 Tf
0 Tc 9.1 0 0 9.1 315.27 318.97 Tm
(0 )Tj
/T1_2 1 Tf
0.05 Tc 11.3452 0 0 8.9 323.68 318.97 Tm
(if )Tj
/T1_0 1 Tf
12.7754 0 0 9.1 332.64 318.97 Tm
(sf )Tj
9.566 0 0 9.1 345.22 318.97 Tm
(m. )Tj
10.1403 0 0 9 23.35 302.77 Tm
(Proof: )Tj
0.0407 Tc 9 0 0 9 61.17 302.77 Tm
(We )Tj
0.0314 Tc 6.669 0 Td
(show )Tj
0.05 Tc 10.0691 0 0 9 144.7 302.77 Tm
(that )Tj
/T1_4 1 Tf
-0.035 Tc 7.3802 0 0 11.6 227.62 284.59 Tm
(o. )Tj
/T1_0 1 Tf
0.0239 Tc 9 0 0 9 23.42 258.31 Tm
(Since )Tj
/T1_2 1 Tf
0 Tc 8.7 0 0 8.7 48.09 258.31 Tm
(s )Tj
/T1_3 1 Tf
12.7 0 0 12.7 55.23 258.31 Tm
(f )Tj
/T1_0 1 Tf
0.05 Tc 9.566 0 0 9 61.18 258.31 Tm
(m, )Tj
9.0703 0 0 9 75.95 258.31 Tm
(we )Tj
9.2091 0 0 9 90.99 258.31 Tm
(can )Tj
0.0236 Tc 9 0 0 9 108.44 258.31 Tm
(find )Tj
0.05 Tc 9.4249 0 0 9 136.27 258.31 Tm
(prime )Tj
0.016 Tc 8.7 0 0 8.7 163.22 258.31 Tm
(PI )Tj
-0.035 Tc 6.2928 0 0 12.3 175.8 258.31 Tm
(cF )Tj
/T1_2 1 Tf
-0.0235 Tc 9.1 0 0 9.1 185.89 258.31 Tm
(p, )Tj
/T1_0 1 Tf
0.05 Tc 9.1649 0 0 9 196.83 258.31 Tm
(and )Tj
/T1_1 1 Tf
0 Tc 9.3 0 0 9.3 215.37 258.31 Tm
(k )Tj
/T1_0 1 Tf
9 0 0 9 223.87 258.31 Tm
(E )Tj
0.05 Tc 9.3847 0 0 9 23.32 246.97 Tm
(Then )Tj
9.2738 0 0 9 245.15 258.49 Tm
(with )Tj
/T1_2 1 Tf
0 Tc 8.8 0 0 8.8 267.33 258.49 Tm
(s )Tj
/T1_0 1 Tf
0.05 Tc 9.7016 0 0 9 23.54 131.41 Tm
(But )Tj
0.0402 Tc 9 0 0 9 42.02 131.41 Tm
(every )Tj
0.05 Tc 9.7771 0 0 9 66.82 131.41 Tm
(summand )Tj
0.0074 Tc 9 0 0 9 110.79 131.41 Tm
(of )Tj
0.05 Tc 9.1661 0 0 9 121.66 131.41 Tm
(this )Tj
9.2323 0 0 9 140.14 131.41 Tm
(last )Tj
9.6166 0 0 9 158.44 131.41 Tm
(sum )Tj
-0.0299 Tc 9 0 0 9 178.67 131.41 Tm
(is )Tj
0.0173 Tc 1.062 0 Td
(zero )Tj
0.05 Tc 9.1696 0 0 9 207.73 131.41 Tm
(by )Tj
9.4511 0 0 9 220.81 131.41 Tm
(Lemma )Tj
-0.035 Tc 8.8645 0 0 9 254.59 131.41 Tm
(6. )Tj
0 Tc 12.9 0 0 12.9 366.89 130.87 Tm
(o )Tj
0.05 Tc 9.1159 0 0 9 37.9 106.57 Tm
(Thus )Tj
9.2348 0 0 9 62.36 106.57 Tm
(Conditions )Tj
0 Tc 9 0 0 9 111.86 106.57 Tm
(7 )Tj
0.05 Tc 9.5174 0 0 9 120.32 106.57 Tm
(and )Tj
0 Tc 9 0 0 9 139.7 106.57 Tm
(8 )Tj
0.05 Tc 9.298 0 0 9 148.49 106.57 Tm
(need )Tj
9.0633 0 0 9 171.63 106.57 Tm
(only )Tj
9.152 0 0 9 193.15 106.57 Tm
(be )Tj
0.0313 Tc 9 0 0 9 206.73 106.57 Tm
(checked )Tj
0.0274 Tc 3.879 0 Td
(for )Tj
0.05 Tc 9.2082 0 0 9 257.38 106.57 Tm
(those )Tj
8.2267 0 0 6 283.21 106.57 Tm
(5, )Tj
/T1_2 1 Tf
0 Tc 10.3 0 0 10.3 294.54 106.57 Tm
(t )Tj
/T1_0 1 Tf
0.05 Tc 9.5548 0 0 9 302.21 106.57 Tm
(with )Tj
/T1_2 1 Tf
8.0599 0 0 6.7 325.35 106.57 Tm
(8pt )Tj
/T1_3 1 Tf
0 Tc 12.7 0 0 12.7 342.01 106.57 Tm
(I )Tj
/T1_2 1 Tf
0.05 Tc 9.6463 0 0 9.2 347.89 106.57 Tm
(n. )Tj
/T1_0 1 Tf
9.3287 0 0 9 363 106.57 Tm
(In )Tj
9.1833 0 0 9 23.59 95.22 Tm
(particular, )Tj
10.1089 0 0 9 69.82 95.22 Tm
(the )Tj
9.1024 0 0 9 87.29 95.22 Tm
(resulting )Tj
9.1647 0 0 9 126.99 95.22 Tm
(direct )Tj
9.6166 0 0 9 154.3 95.22 Tm
(sum )Tj
0.0274 Tc 9 0 0 9 174.87 95.22 Tm
(of )Tj
0.0344 Tc 1.251 0 Td
(basic )Tj
0.0468 Tc 2.62 0 Td
(pairs )Tj
0.05 Tc 9.4161 0 0 9 233.19 95.22 Tm
(constructed )Tj
9.1577 0 0 9 285.21 95.22 Tm
(only )Tj
0.0357 Tc 9 0 0 9 306.83 95.22 Tm
(involves )Tj
0.0338 Tc 4.017 0 Td
(finitely )Tj
0.05 Tc 9.3594 0 0 9 23.56 83.89 Tm
(many )Tj
0.0494 Tc 9 0 0 9 48.97 83.89 Tm
(basic )Tj
0.05 Tc 9.2479 0 0 9 72.73 83.89 Tm
(pairs. )Tj
/T1_3 1 Tf
0.0206 Tc 7.8001 0 0 7.8001 194.52 47.89 Tm
(236 )Tj
ET
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