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Linear congruences and a conjecture of Bibak

Chinnakonda Gnanamoorthy Karthick BabuRanjan BeraBalasubramanian Sury — 2024

Czechoslovak Mathematical Journal

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 i = 1 k a i x i b ( mod n ) . In particular, we obtain explicit expressions for the number of solutions, where x i ’s are squares modulo n . In addition, we obtain expressions for the number of solutions with order restrictions x 1 x k or with strict order restrictions x 1 > > x k in some special cases. In these results, the expressions for the number of solutions involve Ramanujan...

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