MathLabs

Problem 4

Determine all pairs (a,b)(a,b) of positive integers such that ab2+b+7 ab^{2}+b+7 divides a2b+a+b a^{2}b+a+b .
Step 6 of 6: State all solutions
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In plain words

Collect the cases.

(a,b)=(11,1),(49,1),(7t2,7t)(a,b)=(11,1),(49,1),(7t^2,7t)
Detailed analysis

Direct substitution verifies (11,1)(11,1) and (49,1)(49,1), and the zero-remainder computation verifies the infinite family. These are all the solutions.