Linear congruences and a conjecture of Bibak
We address three questions posed by K. Bibak (2020), and generalize some results of K. Bibak, D. N. Lehmer and K. G. Ramanathan on solutions of linear congruences . In particular, we obtain explicit expressions for the number of solutions, where ’s are squares modulo . In addition, we obtain expressions for the number of solutions with order restrictions or with strict order restrictions in some special cases. In these results, the expressions for the number of solutions involve Ramanujan...