Math Problem Statement

find the total number of integral solutions (a, b) of (7 โˆ’ ๐‘Ž๐‘)^2/๐‘Ž^2+b^2 = 1

Solution

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Math Problem Analysis

Mathematical Concepts

Diophantine Equations
Algebra
Integer Solutions

Formulas

(7 - ab)^2 / (a^2 + b^2) = 1
a^2b^2 - a^2 - b^2 - 14ab + 49 = 0

Theorems

Diophantine equation theory
Trial and error for integer solutions

Suitable Grade Level

Grades 10-12