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Old 2019-01-18, 12:11   #2
ATH
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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 2019-01-18 at 12:16
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