34x=41n+5, x=((34+7)n+5)/34=n+7n/34+5/34=n+(7n+5)/34 We require 7n+5 to be a multiple of 34. 7n+5=34, 7n+5=68, 7n=63 so n=9. 34x=41×9+5=369+5=374, x=11. An integer below 40 satisfying 34x=5(mod 41) is x=11. 34×11=374=5(mod 41) because 374/41=9 rem 5.
