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DTSTART:20250309T070000
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DTSTART;TZID=America/Toronto:20251001T143000
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URL:https://uwaterloo.ca/pure-mathematics/events/number-theory-seminar-149
SUMMARY:Number Theory Seminar
CLASS:PUBLIC
DESCRIPTION:KARL DILCHER\, DALHOUSIE UNIVERSITY\n\n_Heronian triangles\, Ga
 uss primes\, and some linear recurrences_\n\nWe will see that certain sequ
 ences of Heronian triangles\, that is\,\ntriangles with sides of integer l
 ength and with integer area\, occur in\nan unexpected way in the study of 
 some specific factorials. In\nparticular\, we will consider the multiplica
 tive order of ((p-1)/4)!\nmodulo a prime p = 1 (mod 4). The question of wh
 en this order can be a\npower of 2 leads to the concept of a \"Gauss prime
 \". Apart from\nexplaining these various connections\, I will derive some 
 divisibility\nproperties of the sequences in question. \n\nTime allowing\,
  I will also discuss factorials ((p-1)/3)! modulo primes\np = 1 (mod 6)\, 
 and generalizations of such factorials. Quite recently\,\na close relatio
 nship between \"exceptional primes\" in this setting and\nIwasawa theory w
 as established by M. Stokes in his Ph.D. thesis.\n\n(Joint work with John 
 Cosgrave.)\n\nMC 4064
DTSTAMP:20260408T022756Z
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