Geodesic
Perfect difference sets
Glasgow mathematical journal, Tome 6 (1964) no. 4, pp. 177-184

Voir la notice de l'article provenant de la source Cambridge University Press

If the set K of r+1 distinct integers k0, k1 ..., kr has the property that the (r+1)r differences ki–kj (0≦i, j≦r, i≠j) are distinct modulo r2+r+1, K is called a perfect difference set modr2+r+1. The existence of perfect difference sets seems intuitively improbable, at any rate for large r, but in 1938 J. Singer [1] proved that, whenever r is a prime power, say r = pn, a perfect difference set mod p2n+pn+1 exists. Since the appearance of Singer's paper several authors have succeeded in showing that for many kinds of number r perfect difference sets mod r2+r+1 do not exist; but it remains an open question whether perfect difference sets exist only when r is a prime power (for a comprehensive survey see [2]). 
Halberstam, H.; Laxton, R. R. Perfect difference sets. Glasgow mathematical journal, Tome 6 (1964) no. 4, pp. 177-184. doi: 10.1017/S2040618500034985
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