MathLabs

Problem 2

Determine all pairs of positive integers (a,b)(a,b) such that a22ab2−b3+1\frac{a^2}{2ab^2-b^3+1} is a positive integer.
Step 1 of 3: Start with b=1b=1
Previous stepNext step
In plain words

Start with b=1b=1

a=2kwhenb=1a=2k when b=1
Detailed analysis

When b=1b=1, the denominator is 2a2a, so the quotient is a/2a/2. It is a positive integer exactly when a=2ta=2t for a positive integer tt, giving (a,b)=(2t,1)(a,b)=(2t,1).