On the Congruence System X ≡ A_1[b_1] and αx ≡ A_2[b_2] Such that αb_1 ≡ ± (10 /p) [b_2] with P ∈ {1, 2, 5, 10}

Algoni Mohamed

On the Congruence System X ≡ A_1[b_1] and αx ≡ A_2[b_2] Such that αb_1 ≡ ± (10 /p) [b_2] with P ∈ {1, 2, 5, 10}

We propose a method to solve the modular equation system:x ≡ a_1[b_1]αx ≡ a_2[b_2]with α, a_1, a_2, b_1 and b_2 ∈ N∗ such that a_2 ≥ αa_1 and αb_1 ≡ ±(10/p)[b_2] with p ∈ {1, 2, 5, 10}This method is based on our latest work "On the Diophantine equation ax+by=c with a ≡ ±(10/p)[b] and p ∈ {1, 2, 5, 10}". It is therefore based on the analysis of the units of products pb_2 and p(a_2 − αa_1), which we designate respectively by u and uu2032 .

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[v1] 2025-01-08 21:32:08

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Number Theory

On the Congruence System X ≡ A_1[b_1] and αx ≡ A_2[b_2] Such that αb_1 ≡ ± (10 /p) [b_2] with P ∈ {1, 2, 5, 10}

Submission history