An estimate is given of the size of a positive integer solution $n$ of the inequality $phi(an+b)<phi(an)$, $gcd(a,b)=1$. Experiments indicate that this gives a useful indication of the size of the {em minimal} solution.

Numerical Algorithms and Problems (acm F.2.1)
Arithmetic functions; related numbers; inversion formulas (msc 11A25), Values of arithmetic functions; tables (msc 11Y70)
Life Sciences (theme 5), Energy (theme 4)
Cornell University Library e-Print archive
Scientific Computing

te Riele, H.J.J. (2001). On the size of solutions of the inequality ø(ax+b)<ø(ax). e-Print archive. Cornell University Library .