# On the Oesterlé-Masser conjecture

@article{Stewart1986OnTO,
title={On the Oesterl{\'e}-Masser conjecture},
author={C. L. Stewart and Robert Tijdeman},
journal={Monatshefte f{\"u}r Mathematik},
year={1986},
volume={102},
pages={251-257}
}
• Published 1 September 1986
• Mathematics
• Monatshefte für Mathematik
Letx, y andz be positive integers such thatx=y+z and ged (x,y,z)=1. We give upper and lower bounds forx in terms of the greatest squarefree divisor ofx y z.
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## References

SHOWING 1-8 OF 8 REFERENCES