Math Problem Statement

Use the theory of congruence to show that 7|5^2n + 3.2^(5n-2)

Solution

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Math Problem Analysis

Mathematical Concepts

Modular Arithmetic
Exponentiation
Congruences
Divisibility

Formulas

a ≡ b (mod n)
5^6 ≡ 1 (mod 7)
2^3 ≡ 1 (mod 7)

Theorems

Periodicity in Modular Arithmetic
Modular Exponentiation

Suitable Grade Level

Grades 11-12