41*21 = 1 (mod 43) so 41^(1) = 21 (mod 43):
41s+1:

41s+1 = 0 (mod 43) => 41s = 1 (mod 43) => s=(1)*41^(1) = (1)*21 = 21 = 22 (mod 43).
so s=22+43n and the numbers are then: 41*(43n+22)+1 = 1763n+903
41s+10:

41s+10 = 0 (mod 43) => 41s = 33 (mod 43) => s=33*21 = 5 (mod 43)
so s=5+43n and the numbers are then: 41*(43n+5)+10 = 1763n+215
41s+16:

41s+16 = 0 (mod 43) => 41s = 27 (mod 43) => s=27*21 = 8 (mod 43)
so s=8+43n and the numbers are then: 41*(43n+8)+16 = 1763n+344
41s+18:

41s+18 = 0 (mod 43) => 41s = 25 (mod 43) => s=25*21 = 9 (mod 43)
so s=9+43n and the numbers are then: 41*(43n+9)+18 = 1763n+387
41s+37:

41s+37 = 0 (mod 43) => 41s = 6 (mod 43) => s=6*21 = 40 (mod 43)
so s=40+43n and the numbers are then: 41*(43n+40)+37 = 1763n+1677
So 1763n + m, where m is 215,344,387,903,1677
Last fiddled with by ATH on 20190118 at 12:16
