MathDB
Number of quadruples and divisibility

Source: Baltic Way 2014, Problem 18

November 11, 2014
symmetryabstract algebramodular arithmeticnumber theory proposednumber theory

Problem Statement

Let pp be a prime number, and let nn be a positive integer. Find the number of quadruples (a1,a2,a3,a4)(a_1, a_2, a_3, a_4) with ai∈{0,1,…,pn−1}a_i\in \{0, 1, \ldots, p^n - 1\} for i=1,2,3,4i = 1, 2, 3, 4, such that pn∣(a1a2+a3a4+1).p^n \mid (a_1a_2 + a_3a_4 + 1).
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